The study assessed the conceptual understanding and attitude toward fractions of teacher education students in a socio-constructivist learning environment. Specifically, it determined the students’ level of conceptual understanding before and after instruction; verified the types of conceptual changes that occurred; and ascertained the attitude of students toward fractions before and after instruction and its relationship to their levels of understanding. Descriptive-correlational research method was used. Socio-constructivist context-based teaching method was employed to introduce the concept of fractions. Achievement (...) tests and interviews were administered to determine the students’ level of conceptual understanding. Conceptual analysis based on Jensen and Finley’s (1995) method with Tiberghien’s (1994) classification of changes was utilized to describe students’ conceptual understanding and conceptual changes. In order to determine their attitude on fractions, students were asked to answer the socio-constructivist attitude questionnaire. The level of conceptual understanding of teacher education students in fraction was functional misconception and partial understanding before and after instruction, respectively. The type of conceptual change that occurred among teacher education students was change for the better. Socio-constructivist learning more likely to improve students’ attitudes toward fractions; promoted prosocial behavior among students; and tend to increase students’ activeness in the classroom activities as evidenced. (shrink)

I conjecture that the probability amplitudes of a quantum state are fractions of the Planck frequency, stemming from the rich dynamics at the Planck scale. This offers a means to indirectly measure the fundamental properties of quantum spacetime and potentially resolves the measurement problem.

The necessity for a government “lender of last resort” has been advanced as a justification for central banking. In this paper, I compare lending practices under central banking with those that would be likely to exist under a system of fractional-reserve free banking (FRFB). To do this I examine the underlying nature of banks as warehousing and credit-granting institutions and consider how redemption runs can arise as a consequence of fractional reserves in this system. Following the work of Thornton and (...) Bagehot, I describe principles of prudent lending that can be used to stem a redemption run when it arises. I examine the market incentives that apply under FRFB and how these incentives are perverted under a system of central banking. I find that a government central bank is not well-placed to lend according to prudent standards, and in fact is likely to use its power to pursue political goals that are at odds with prudent lending. I examine the US financial crisis and the actions of the Federal Reserve System to illustrate this view. (shrink)

Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given (...) for claiming that syllogistic validity is relevant validity. (shrink)

Abstract: In this paper, the definition of triple Aboodh transform of fractional order α, where α ϵ [0, 1], is introduced for functions which are fractional differentiable. We also present several properties of this transform. Furthermore, some main theorems and their proofs are discussed.

The difficulty of primary students in solving simple fractions is because students fail to understand the concept of simple fractions. Meanwhile, the results of previous studies allow the integration of PowToon animation multimedia into a constructivist approach to facilitate the conception of the simple fraction. This research aims to develop constructivist-based PowToon animation multimedia (CoPAM) as a valid, practical, and effective learning media for simple fraction material. PowToon was developed using a research and development (R&D) method with a (...) define, design, and development (3-D) model that involved 12 fourth-grade primary students. The data analysis used was descriptive analysis with data collection methods using observation, tests (pre-test and post-test), validation questionnaires (validation of media and material experts, teacher responses, and student responses), and documentation. The results showed that CoPAM has very feasible product criteria for validity, practicality, and effectiveness to facilitate primary students in understanding simple fractions. The recommendations for the next study are needed to further develop and test CoPAM products or the like (which could go through the dissemination stage) by involving a larger and wider number of participants by testing inferential statistics. (shrink)

An ongoing mystery in sensory science is how sensation magnitude F(I), such as loudness, increases with increasing stimulus intensity I. No credible, direct experimental measures exist. Nonetheless, F(I) can be inferred algebraically. Differences in sensation have empirical (but non-quantifiable) minimum sizes called just-noticeable sensation differences, ∆F, which correspond to empirically-measurable just-noticeable intensity differences, ∆I. The ∆Is presumably cumulate from an empirical stimulus-detection threshold I_th up to the intensity of interest, I. Likewise, corresponding ∆Fs cumulate from the sensation at the stimulus-detection (...) threshold, F(I_th ), up to F(I). Regarding the ∆Is, however, it is unlikely that all of them will be known experimentally; the procedures are too lengthy. The customary approach, then, is to find ∆I at a few widely-spaced intensities, and then use those ∆Is to interpolate all ∆Is using some smooth continuous function. The most popular of those functions is Weber’s Law, ∆I⁄I=K. But that is often not even a credible approximation to the data. However, there are other equations for ∆I⁄I. Any such equation for ∆I⁄I can be combined with any equation for ∆F, through calculus, to altogether obtain F(I). Here, two assumptions for ∆F are considered: ∆F=B (Fechner’s Law) and (∆F⁄F)=g (Ekman’s Law). The respective integrals involve lower bounds I_th and F(I_th ). This stands in broad contrast to the literature, which heavily favors non-bounded integrals. We, hence, obtain 24 new, alternative equations for sensation magnitude F(I) (12 equations for (∆I⁄I) × 2 equations for ∆F). (shrink)

Mathematics is considered one of the most challenging courses for many elementary pre-service teachers (EPTs). In hopes for improvement, teacher educators have been incorporating a jigsaw strategy to equip future teachers with the necessary competencies. Hence, the study aimed to determine the effectiveness of the jigsaw strategy with EPTs’ level of mathematics achievement and interest in an online cooperative learning environment. The research utilized a pre-experimental design with 40 participants. The researchers used pretest and posttest questions covering fraction operations and (...) a mathematics interest questionnaire before and after the intervention. With the implementation of the jigsaw strategy, results showed that the EPTs’ mathematics achievement improved while their interest in mathematics improved to some extent. Likewise, a significant difference between the pre-and post-intervention concerning the EPTs’ mathematics achievement and interest in mathematics was found. Furthermore, correlation analysis revealed that study time is negatively related to mathematics achievement, as is the overall level of interest in mathematics. These findings imply that a jigsaw strategy is a useful tool in teaching mathematics online. However, several modifications may be considered to recognize that the EPTs’ interest in mathematics varies from one person to another. Teacher education institutions are encouraged to apply this strategy not only for EPTs to increase their mathematical know-hows but also to serve as an example for them to employ in their future teaching careers. (shrink)

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties of (...) energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

A puzzle concerning fractional and mixed numbers of things (e.g., two and a half oranges) is examined.

PURPOSE—A substantial fraction of the observations made by clinicians and entered into patient records are expressed by means of negation or by using terms which contain negative qualifiers (as in “absence of pulse” or “surgical procedure not performed”). This seems at first sight to present problems for ontologies, terminologies and data repositories that adhere to a realist view and thus reject any reference to putative non-existing entities. Basic Formal Ontology (BFO) and Referent Tracking (RT) are examples of such paradigms. The (...) purpose of the research here described was to test a proposal to capture negative findings in electronic health record systems based on BFO and RT. METHODS—We analysed a series of negative findings encountered in 748 sentences taken from 41 patient charts. We classified the phenomena described in terms of the various top-level categories and relations defined in BFO, taking into account the role of negation in the corresponding descriptions. We also studied terms from SNOMED-CT containing one or other form of negation. We then explored ways to represent the described phenomena by means of the types of representational units available to realist ontologies such as BFO. RESULTS—We introduced a new family of ‘lacks’ relations into the OBO Relation Ontology. The relation lacks_part, for example, defined in terms of the positive relation part_of, holds between a particular p and a universal U when p has no instance of U as part. Since p and U both exist, assertions involving ‘lacks_part’ and its cognates meet the requirements of positivity. CONCLUSION—By expanding the OBO Relation Ontology, we were able to accommodate nearly all occurrences of negative findings in the sample studied. (shrink)

The problem of moral luck is that a general fact about luck and an intuitive moral principle jointly imply the following skeptical conclusion: human beings are morally responsible for at most a tiny fraction of each action. This skeptical conclusion threatens to undermine the claim that human beings deserve their respective eternal reward and punishment. But even if this restriction on moral responsibility is compatible with the doctrine of the final judgment, the quality of one’s afterlife within heaven or hell (...) still appears to be lucky. Utilizing recent responses to the problem of moral luck, I explore several Molinist accounts of the final judgment that resolve both theological problems of moral luck. Some of these accounts entirely eliminate moral luck while others ensure that the moral luck involved in the judgment is overall good luck. (DOWNLOAD the published version at the external link below.). (shrink)

This article first describes a dilemma for liberalism: On the one hand restricting their own options is an important means for groups of people to shape their lives. On the other hand, group members are typically divided over whether or not to accept option-restricting solutions or policies. Should we restrict the options of all members of a group even though some consent and some do not? This dilemma is particularly relevant to public health policy, which typically target groups of people (...) with no possibility for individuals to opt out. The article then goes on to propose and discuss a series of aggregation rules for individual into group consent. Consideration of a number of scenarios shows that such rules cannot be formulated only in terms of fractions of consenters and non-consenters, but must incorporate their motives and how much they stand to win or lose. This raises further questions, including what is the appropriate impact of altruistic consenters and non-consenters, what should be the impact of costs and benefits and whether these should be understood as gross or net. All these issues are dealt with in a liberal, anti-paternalistic spirit, in order to explore whether group consent can contribute to the justification of option-restricting public health policy. (shrink)

One of the most influential recent developments in supposedly radical philosophy is ‘posthumanism’. This can be seen as the successor to ‘deconstructive postmodernism’. In each case, the claim of its proponents has been that cultures are oppressive by virtue of their elitism, and this elitism, fostered by the humanities, is being challenged. In each case, however, these philosophical ideas have served ruling elites by crippling opposition to their efforts to impose markets, concentrate wealth and power and treat everyone and everything (...) as mere instruments in a way that is not only undermining democracy and threatening economic, social and political stability through growing inequality, but is crippling efforts to deal with the global ecological crisis. Philosophers, Nietzsche claimed, are physicians of culture. Why should people claiming to be philosophers, or at least aligned with philosophers, subvert their own calling? In this paper I will suggest that with the expansion of education and the rise of neoliberalism, those involved in education and research, particularly in the humanities and social sciences, have been proletarianized, and most have accepted this proletarianization. They have been reduced to a fraction of the proletariat - wage-slaves without economic security and therefore dependent on the will of others on whom they are dependent. They are not ordinary wage-slaves, however, but wage-house-slaves, having salaries rather than wages. If, as Marx argued, social being determines consciousness, posthumanism can be understood as the expression of ressentiment of these house-slaves at their condition while simultaneously serving to affirm their superiority to field-slaves while serving their masters. Their work is supported because it provides ideological cover for their masters, the new transnational managerial class or corporatocracy as they expand their power through information technology, while absolving this corporatocracy from responsibility for the consequences of their growing power. In making this claim I will argue that the real target of deconstructionists and posthumanists, although this is now seldom appreciated, has been the humanism of the New Left, a revival of the Radical Enlightenment inspired by Renaissance civic humanism and the German Renaissance. (shrink)

Health policy is only one part of social policy. Although spending administered by the health sector constitutes a sizeable fraction of total state spending in most countries, other sectors such as education and transportation also represent major portions of national budgets. Additionally, though health is one important aspect of economic and social activity, people pursue many other goals in their social and economic lives. Similarly, direct benefits—those that are immediate results of health policy choices—are only a small portion of the (...) overall impact of health policy. This chapter considers what weight health policy should give to its “spill-over effects,” namely non-health and indirect benefits. (shrink)

It is commonplace in discussions of modern cosmology to assert that the early universe began in a special state. Conventionally, cosmologists characterize this fine-tuning in terms of the horizon and flatness problems. I argue that the fine-tuning is real, but these problems aren't the best way to think about it: causal disconnection of separated regions isn't the real problem, and flatness isn't a problem at all. Fine-tuning is better understood in terms of a measure on the space of trajectories: given (...) reasonable conditions in the late universe, the fraction of cosmological histories that were smooth at early times is incredibly tiny. This discussion helps clarify what is required by a complete theory of cosmological initial conditions. (shrink)

Every account of moral responsibility has conditions that distinguish between the consequences, actions, or traits that warrant praise or blame and those that do not. One intuitive condition is that praiseworthiness and blameworthiness cannot be affected by luck, that is, by factors beyond the agent’s control. Several philosophers build their accounts of moral responsibility on this luck-free condition, and we may call their views Luck-Free Moral Responsibility (LFMR). I offer moral and metaphysical arguments against LFMR. First, I maintain that considerations (...) of fairness that often motivate LFMR do not require its adoption. Second, I contend that LFMR has counterintuitive implications for the nature and scope of praiseworthiness and blameworthiness and that LFMR is vulnerable to a reductio ad absurdum. Third, I state some common reasons for thinking that LFMR’s commitment to true counterfactuals of libertarian freedom is problematic, and I argue that if there are no such true counterfactuals and if LFMR is true, a person is praiseworthy and blameworthy at most for a tiny fraction of her actions. Fourth, I argue that proponents of LFMR cannot escape this skeptical cost by appealing to a different kind of counterfactual of freedom. Fifth, I develop an anti-skeptical motivation to affirm the idea that luck can affect moral responsibility. (shrink)

While COVID-19 vaccines provide light at the end of the tunnel in a difficult time, they also bring forth the complex ethical issue of global vaccine distribution. The current unequal global distribution of vaccines is unjust towards the vulnerable living in low-income countries. A vaccine tax should be introduced to remedy this. Under such a scheme, a small fraction of the money spent by a country on vaccines for its own population would go into a fund, such as COVAX, dedicated (...) to buying vaccines and distributing them to the world’s poorest. A vaccine tax would provide a much-needed injection of funds to remedy the unequal distribution of vaccines. The tax allows for a distribution that, to a lesser degree, reflects the ability to pay and is superior to a donation-based model because it minimises the opportunity for free-riding. (shrink)

In this commentary, I explore the ongoing debate surrounding Bangladesh’s electoral reform as the interim government has launched a commission to examine alternatives to the First-Past-the-Post (FPTP) system. Proponents of Proportional Representation (PR) argue it could lead to fairer, more inclusive representation by better reflecting each party’s share of the vote. However, the reality is more complex: PR risks unintended consequences like weakened governance, legitimacy issues that may challenge democratic principles, and technical problems such as the “rounding problem,” where minor (...) vote fractions can affect seat allocation. While the PR system sounds promising, especially to address concerns about the over-centralization of power, it’s essential to critically assess how this model might impact Bangladesh’s unique political landscape. (shrink)

A heuristic is a rule of thumb. In psychology, heuristics are relatively simple rules for making judgments. A fast heuristic is easy to use and allows one to make judgments quickly. A frugal heuristic relies on a small fraction of the available evidence in making judgments. Typically, fast and frugal heuristics (FFHs) have, or are claimed to have, a further property: They are very reliable, yielding judgments that are about as accurate in the long run as ideal non-fast, non-frugal rules. (...) This paper introduces some well-known examples of FFHs, raises some objections to the FFH program, and looks at the implications of those parts of the FFH program about which we can have some reasonable degree of confidence. (shrink)

Rules are meant to apply equally to all within their jurisdiction. However, some rules are frequently broken without consequence for most. These rules are only occasionally enforced, often at the discretion of a third-party observer. We propose that these rules—whose violations are frequent, and enforcement is rare—constitute a unique subclass of explicitly codified rules, which we call ‘phantom rules’ (e.g., proscribing jaywalking). Their apparent punishability is ambiguous and particularly susceptible to third-party motives. Across six experiments, (N = 1440) we validated (...) the existence of phantom rules and found evidence for their motivated enforcement. First, people played a modified Dictator Game with a novel frequently broken and rarely enforced rule (i.e., a phantom rule). People enforced this rule more often when the “dictator” was selfish (vs. fair) even though the rule only proscribed fractional offers (not selfishness). Then we turned to third person judgments of the U.S. legal system. We found these violations are recognizable to participants as both illegal and commonplace (Experiment 2), differentiable from violations of prototypical laws (Experiments 3) and enforced in a motivated way (Experiments 4a and 4b). Phantom rule violations (but not prototypical legal violations) are seen as more justifiably punished when the rule violator has also violated a social norm (vs. rule violation alone)—unless the motivation to punish has been satiated (Experiment 5). Phantom rules are frequently broken, codified rules. Consequently, their apparent punishability is ambiguous, and their enforcement is particularly susceptible to third party motives. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were (...) exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

The idea that the brain is a representational organ has roots in the nineteenth century, when neurologists began drawing conclusions about what the brain represents from clinical and experimental studies. One of the earliest controversies surrounding representation in the brain was the “muscles versus movements” debate, which concerned whether the motor cortex represents complex movements or rather fractional components of movement. Prominent thinkers weighed in on each side: neurologists John Hughlings Jackson and F.M.R. Walshe in favor of complex movements, neurophysiologist (...) Charles Sherrington and neurosurgeon Wilder Penfield in favor of movement components. This essay examines these and other brain scientists’ evolving notions of representation during the first eighty years of the muscles versus movements debate (c. 1873–1954). Although participants agreed about many of the superficial features of representation, their inferences reveal deep-seated disagreements about its inferential role. Divergent epistemological commitments stoked conflicting conceptions of what representational attributions imply and what evidence supports them. (shrink)

In the last 20 years, a stream of research emerged under the label of „complex problem solving“ (CPS). This research was intended to describe the way people deal with complex, dynamic, and intransparent situations. Complex computer-simulated scenarios were as stimulus material in psychological experiments. This line of research lead to subtle insights into the way how people deal with complexity and uncertainty. Besides these knowledge-rich, realistic, intransparent, complex, dynamic scenarios with many variables, a second line of research used more simple, (...) knowledge-lean scenarios with a low number of variables („minimal complex systems“, MCS) that have been proposed recently in problem-solving research for the purpose of educational assessment. In both cases, the idea behind the use of microworlds is to increase validity of problem solving tasks by presenting interactive environments that can be explored and controlled by participants while pursuing certain action goals. The main argument presented here is: both types of systems - CPS and MCS – can only be dealt with successfully if causal dependencies between input and output variables are identified and used for system control. System knowledge is necessary for control and intervention. But CPS and MCS differ in their way of how causal dependencies are identified and how the mental model is constructed; therefore, they cannot be compared directly to each other with respect to the cognitive processes that are necessary for solving the tasks. Knowledge-poor MCS tasks address only a small fraction of the cognitive processes and structures needed for knowledge-rich CPS situations. (shrink)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

ABSTRACT: Almost all the voices of the six million Jewish men, women, and children who perished in the Holocaust were shuttered in the massacres of the Einsatzgruppen and inside the gas chambers (and vans) of the six German extermination camps (Auschwitz-Birkenau, Treblinka II, Bełżec, Sobibór, Chełmno, and Majdanek). Some of the victims' writings and drawings have survived, and these testimonies remain today a fraction of the millions of voices that were lost forever. With this paper I would like to convey (...) the idea that the (reconstructed and often fictionalized) voices that can be found in Holocaust feature films represent a homage to the victims who perished, and that these films (independently of their commercial success or their minor historical errors) often bring knowledge about the victims' suffering, antisemitism, the ghettos, the transports, the massacres, the Vernichtungslager and the Konzentrationslager to the vast public, and represent a glimpse into the shuttered voices of the Shoah. I also argue that, approached with caution, Holocaust films (antisemitic German propaganda films, post-war documentaries and post-war feature films) can be a valuable contribution to the historiography of the Shoah. (shrink)

Parts of the genome of a single individual can have conflicting interests, depending on which parent they were inherited from. One mechanism by which these conflicts are expressed in some taxa, including mammals, is genomic imprinting, which modulates the level of expression of some genes depending on their parent of origin. Imprinted gene expression is known to affect body size, brain size, and the relative development of various tissues in mammals. A high fraction of imprinted gene expression occurs in the (...) brain. Biologists including Hamilton, Trivers and Haig have proposed that this may explain some intrapersonal conflict in humans. This speculation amounts to an inference from conflict within the genome to conflict within the brain or mind. This is a provocative proposal, which deserves serious attention. In this paper I assess aspects of Haig’s version of the proposal. I argue, first, that the notion that intragenomic conflict predicts personal inconsistency should be rejected. Second, while it is unlikely that it credibly predicts sub-personal agents representing conflicting genetic interests, it is plausible that it predicts that the division of cognitive labour could be exploited to turn sub-systems into proxies for conflicting interests. (shrink)

In this paper an attempt has been made towards the design and evaluation of a solar parabolic trough collector (PTC) system integrated with a conventional oil boiler (COB) to increase the energy utilization effectiveness and reduce the environmental emission of the existing conventional oil boiler in the Kombolcha textile factory, in Ethiopia. The factory uses 8500 ton/annum of heavy fuel oil to generate 26 ton/hour of pressurized hot water at 140C temperature which causes an increase in greenhouse gas emissions, so (...) the solar parabolic trough collector hot water generation system will be an appropriate solution for this application. Based on the available annual solar radiation, estimates of the solar fraction, solar energy unit price and system pay-back period have been carried out. The proposed system has the potential to save 1055.9 ton/year of fuel oil. The unit cost of PTC solar energy is estimated to be 0.0088 $/kWh and the payback period of the plant is five years. Since the unit price of oil energy (0.0424 $/kWh) is much greater than the unit price of solar energy by a substantial margin (0.033 $/kWh) in Ethiopia, therefore the water heating system by a solar parabolic trough collector is a feasible alternative to heating by a conventional oil boiler. (shrink)

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general (...) criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)

Perhaps nowhere better than, "On the Names of God," can readers discern Laclau's appreciation of theology, specifically, negative theology, and the radical potencies of political theology. // It is Laclau's close attention to Eckhart and Dionysius in this essay that reveals a core theological strategy to be learned by populist reasons or social logics and applied in politics or democracies to come. // This mode of algorithmically informed negative political theology is not mathematically inert. It aspires to relate a fraction (...) or ratio to a series ... It strains to reduce the decided determinateness of such seriality ever condemned to the naive metaphysics of bad infinity. // It is worth considering that it is the specific 'number' of Dionysius in differential identification with an ineffable god (and, as such, a singular becoming between theology and numbers) that is floating in at least two dimensions [of signification] (be it political Demand on the horizontal dimension or theological Desire on [a] floating dimension) that cannot but *perform the link that relinks* names of god with any political life, populist reason, social justice, or radical democracy straining toward peace. (shrink)

Plantinga develops an ambitious theistic religious epistemology on which theists can have non-inferential knowledge of God. Central to his epistemology is the idea that human beings have a “sensus divinitatis” that produces such knowledge. Recently, several authors have urged an appropriation of the sensus divinitatis that is more friendly to internalist views, such as Phenomenal Conservativism. I argue that this appropriation is too timid and tepid in a variety of ways. It applies only to a small fraction of theistic beliefs; (...) it fails to play the theological role Plantinga intended the sensus divinitatis to play; it fails to imply that most theistic beliefs, most of the time, are justified; when combined with a standard form of Evidentialism, it actually implies that most theistic beliefs are, if justified, inferentially justified; and it is consistent with substantive criticisms of theistic belief originating in work from the Cognitive Science of Religion. (shrink)

This paper investigates how environmental structure, given the innate properties of a population, affects the degree to which this population can adapt to the environment. The model we explore involves simple agents in a 2-d world which can sense a local food distribution and, as specified by their genomes, move to a new location and ingest the food there. Adaptation in this model consists of improving the genomic sensorimotor mapping so as to maximally exploit the environmental resources. We vary environmental (...) structure to see its specific effect on adaptive success. In our investigation, two properties of environmental structure, conditioned by the sensorimotor capacities of the agents, have emerged as significant factors in determining adaptive success: (1) the information content of the environment which quantifies the diversity of conditions sensed, and (2) the expected utility for optimal action. These correspond to the syntactic and pragmatic aspects of environmental information, respectively. We find that the ratio of expected utility to information content predicts adaptive success measured by population gain and information content alone predicts the fraction of ideal utility achieved. These quantitative methods and specific conclusions should aid in understanding the effects of environmental structure on evolutionary adaptation in a wide range of evolving systems, both artificial and natural. (shrink)

The contention discussed here, is that one might be able to get around the puzzle contained in the results of Kim and Chan:— That a quantity of inertial mass is effectively lost, (a so called non-classical-rotational inertia NCRI,) but that being a “supersolid” there is no path for the normal fraction to slip past the 1 – 2 % supersolid fraction, which (it is supposed) remains stationary within the annulus. As a solution we argue that the effective loss of inertial (...) mass might be a real loss of inertial mass– that it might be intrinsic to a supersolid or superfluid “pool,” (a portion which has gone supersolid or superfluid.) In this way the puzzle would be resolved because the normal part and the supersolid part do not need to slip past each other in order to produce the experimental results. (shrink)

My bedroom window is a part of my house, but it is not a partial house. A half-built house is a partial house, but there is no house it is a part of. Being a part of something—parthood—is a familiar topic of philosophical inquiry. Being a partial something—partialhood—is not. The neglect of partialhood is a shame because it is intrinsically interesting as well as metaphysically and semantically important. After using fractions and counting constructions to identify partialhood in §1, I (...) give a theory of the relation in §2-§4. Armed with this theory I turn to applications both in the domain of objects and object-related constructions as well as the domain of events and event-related constructions. In §5 I argue that partialhood allows us to identify a notion of distributivity that helps pinpoint the metaphysical basis of the mass/count distinction. In §6 I argue that the progressive morpheme expresses partialhood; in metaphysical terms, what it is for something to be happening is for there to be a partial event. (shrink)

This is a contribution to the idea that some proofs in first-order logic are synthetic. Syntheticity is understood here in its classical geometrical sense. Starting from Jaakko Hintikka’s original idea and Allen Hazen’s insights, this paper develops a method to define the ‘graphical form’ of formulae in monadic and dyadic fraction of first-order logic. Then a synthetic inferential step in Natural Deduction is defined. A proof is defined as synthetic if it includes at least one synthetic inferential step. Finally, it (...) will be shown that the proposed definition is not sensitive to different ways of driving the same conclusion from the same assumptions. (shrink)

Abstract (for the combined three Parts) This paper presents the simplest known theory of processes involved in a person’s unconscious and conscious achievements such as intending, perceiving, reacting and thinking. The basic principle is that an individual has mental states which possess quantitative causal powers and are susceptible to influences from other mental states. Mental performance discriminates the present level of a situational feature from its level in an individually acquired, multiple featured norm (exemplar, template, standard). The effect on output (...) of a moderate disparity between input and norm is scaled in a universal unit of discrimination (Weber’s fraction), with the norm’s level being zero. When one process converts separate sources of input into an output, their discriminative distances from norm are summated. Distinct processes converging on an output combine their discriminations from norm orthogonally. An output may be influenced by the constructs of other outputs as well as by inputs. Descriptive performance is the influence of one category of input on a verbal output. Reasoning is minimally the effect of one verbal process on another. In deeper mental processing, the influence on a response comes from a response construct modulating a description: this process gives the meaning to an emotion or a motive. Descriptive modulation of stimulation corresponds to a bodily sensation or other conceptualized percept. When an output is explained solely by sources of input, that response to the stimulation may be mediated unconsciously. Development of a person within physical and communal environments embodies such mental causation within material causation and acculturates that mind to social causation. (shrink)

Public funders of health research have been widely criticized on the grounds that their allocations of funding for disease-specific research do not reflect the relative burdens imposed by different diseases. For example, the US National Institutes of Health spends a much greater fraction of its budget on HIV/AIDS research and a much smaller fraction on migraine research than their relative contribution to the US burden of disease would suggest. Implicit in this criticism is a normative claim: Insofar as the scientific (...) opportunities are equal, each patient merits research into their condition proportional to the burden of disease for which that condition is responsible. This claim—the proportional view—is widely accepted but has never been fully specified or defended. In this paper, I explain what is required to specify the view, attempt to do so in the most charitable way, and then critically evaluate its normative underpinnings. I conclude that a severity-weighted proportional view is defensible. I close by drawing out five key lessons of my analysis for health research priority-setting. (shrink)

Surface water sources in the oil producing Niger Delta region of Nigeria are highly susceptible to pollution by petroleum hydrocarbons and so it is important to understand the microbial diversity of such ecosystems. Water and sediment samples were collected between April-August, 2013 from Bodo creeks and taken to Environmental Microbiology laboratory of University of Portharcourt for analysis. A total of thirty aerobic heterotrophic bacterial strains isolated ranged from 3.0 - 7.0 × 104 cfu for surface water and 1.6 - 5.6 (...) × 104 cfu for sediment samples of Bodo creek using serial dilution and spread plate technique. Pure cultures of bacteria were obtained on the basis of their morphological characteristics and subjected to biochemical tests and further classified on the basis of 16S rRNA gene sequence analysis. The DNA was isolated from size fractionated samples and the diversity of bacteria in each fraction was studied using PCR amplification of partial 16S rRNA. The sequences were submitted to NCBIGen bank for identification and assigning of accession numbers. The isolated aerobic heterotrophic bacteria belong to the families of Enterobacteriaceae, Bacilliceae, Alcaligenaceae, Pseudomonadaceae, Flavobactericeae and Planococcaceae. (shrink)

There is a widespread consensus that a commodification of body parts is to be prevented. Numerous policy papers by international organizations extend this view to the blood supply and recommend a system of uncompensated volunteers in this area—often, however, without making the arguments for this view explicit. This situation seems to indicate that a relevant source of justified worry or unease about the blood supply system has to do with the issue of commodification. As a result, the current health minister (...) of Ontario is proposing a ban on compensation even for blood plasma—despite the fact that Canada can only generate 30 % of the plasma needed for fractionation into important plasma protein products and has to purchase the rest abroad. In the following, I am going to suggest a number of alternative perspectives on the debate in order to facilitate a less dogmatic and more differentiated debate about the matter. Especially in light of the often over-simplified notions of altruism and commodification, I conclude that the debate has not conclusively established that it would be morally objectionable to provide blood plasma donors with monetary compensation or with other forms of explicit social recognition as an incentive. This is especially true of donations for fractionation into medicinal products by profit-oriented pharmaceutical companies. (shrink)

Latent heat thermal energy storage technique has demonstrate to be a better engineering option mainly due to its benefit of supplying higher energy storage density in a smaller temperature difference between retrieval and storage. For this purpose, a micro electro-mechanical system, MEMS-based heat exchanger with microencapsulated PCM (MEPCM) slurry as cold fluid, has been simulated three dimensionally. This work investigates the influence of using MEPCM-slurry on the temperature of the cold and hot fluids. The MEPCM and water properties have been (...) considered temperature dependent. MEPCM-slurry is used with different volume fractions. The result shows that using MEPCM with 25% volume fraction leads to the improvement in fluids temperatures, that is, for hot fluid the rate of temperature reduction increases up to 23.5% and for cold fluid the rate of temperature rise decreases to 9%, compared to using only water in the MEMS. (shrink)

In this papers ,we use the control method of the maximal fractional integral and obtain the boundedness of higher order commutator generated by maximal Bochner-Riesz operator on Morrey space. Moreover , we get it's continuty from Morrey space to Lipschtz space and from Morrey space to BMO space.

The geology of Khanozai area is comprised of Indian Platform Sediments, the Suture Zone and Flysch Zone. The Khanozai Ophiolite Complex is a fragment of Zhob Valley ophiolites is marking the Suture Zone in the area and consists of mantle peridotite overlain by crustal ultramafic to mafic cumulate which is underlain by metamorphic sole rocks and mélange. The crustal section of the ophiolite comprises of both ultramafic to mafic cumulates. Ultramafic cumulates comprise repeated successions of dunite, pyroxenite and wehrlite while (...) mafic cumulates consist of foliated to layered gabbros. The Khanozai gabbros cover about 60% area of the crustal plutonic rocks and have a lower transitional contact with the ultramafic cumulates. The gabbros (sensu lato) are classified as olivine gabbro, gabbronorite, olivine gabbronorite, norite and gabbro. The mineralogy of the gabbros indicates that they have both primitive and evolved components. The geochemistry indicates that the Khanozai gabbros are tholeiitic in nature and comprise both cumulate and non-cumulate mineral phases with olivine, pyroxenes and plagioclase being involved in fractionation. The cyclic series of ultramafic cumulates and gabbros has a different order, thickness, and structure in the crustal part of ophiolite and this possibly results from a variable supply of different magma compositions to the chamber. The structure of Khanozai Ophiolite’ crustal section, with a well-developed plutonic sequence and absence of sheeted dyke indicate that these rocks may have formed in a tectonic setting with a slow spreading rate over different periods of time as a consequence of episodic low magma supply rates. These gabbros may have formed in a similar manner to the Semail Ophiolite’ gabbros and imply that a well-developed ophiolitic sequence is rarely formed in a tectonic setting where the spreading and magma supply rates are not balanced. (shrink)

This study was performed on disseminated low-grade chromite ore, Gedarif State, Umm Saqata-Qala Elnahal, to treatment the ore by Heavy media separation (HMS) with low intensity magnetic separation (LIMS) for course fraction size (-212+75) μm and selective flocculation for chromite slimes (-75) μm. The ore of the study area is low grade contains 21.5% Cr2O3 with the liberation size of chromite mineral in the range (0.30-0.05) mm. The main gangue of the ore is mineral silicates as the Antigorite mineral. The (...) ore was crushed, ground, and then classified to tow fraction size (-212+75) μm and slimes (-75) μm. Fractions size (-212+75) μm contained 25.58% Cr2O3 was treated by HMS via Bromofrom mixed with carbon tetrachloride flowed by low intensity magnetic separator. HMS with LIMS obtained the highest recovery 82.52% and grade 46.62% Cr2O3 for chromite concentrate with 2.54 Cr/Fe. The slimes (-75) μm contained 22.17% Cr2O3 was treated by selective flocculation method. Optimum grade 42.71% Cr2O3 and recovery 37.10% for chromite concentrate, were achieved at sodium silicate concentration 100 mg/l, starch concentration 45 mg/l, pH=9, and solid percentage 5%. (shrink)

intro to Part 1 - -/- Most people disliked mathematics when they were at school and they were absolutely correct to do so. This is because maths as we know it is severely incomplete. No matter how elaborated and complicated mathematical equations become, in today's world they're based on 1+1=2. This certainly conforms to the world our physical senses perceive and to the world scientific instruments detect. It has been of immeasurable value to all knowledge throughout history and has elevated (...) science to the lofty status it enjoys. Science is now striving towards Unification - where the subatomic realm, all matter, energy, forces, space and time will be seen as entangled parts of one universe. While 1+1=2 has been vital in getting humanity to this point, it's time to suppress our attachments to the past and realize that whereas 1+1 will always equal 2, it's also capable of equalling the 1 which represents unification. -/- intro to Part 2 -/- b) Division by zero is accepted, in Newtonian maths, to be impossible. But we can regard division by zero as division by nothing i.e. division that has no effect. In this case, 1 divided by 0 is 1. However, to a physicist there is no such thing as nothing (even empty space contains energy). What could the something called 0 actually be? It could be a binary digit. If we use the base of ten (for simplicity) and attach one and zero to it as exponents, we get 10^1 divided by 10^0 = 10^1. If we then cancel 10 from each factor in the expression, we get 1 divided by 0 = 1. At the start of the paragraph, this was referred to as division by nothing. Then 0 was called a binary digit and division by nothing became division by something. The 1 that the division equals is the unified field of space-time. Division by 0 is impossible in Newtonian maths because the result can be infinity. But the word “infinity” can, as the last section of this book shows, apply to the unified field of spacetime. So division by zero is not impossible because it results in the universe, which is obviously possible … a possibility that has always been, and always will be, realized. -/- intro to Part 3 -/- If quantum entanglement has existed in the entire universe forever, everything would be everywhere and everywhen. Space, time and 5th-dimensional hyperspace would not be restricted to certain parts of the Mobius Universe but would exist in every particle. Past, present and future would not exist as the distinct periods which everyday life assumes. All instants of all periods would exist eternally, permitting time travel to any point in the past and to any point in the future. Entanglement may be created by simply zipping along at close to the speed of light - “Quantum entanglement of moving bodies” by Robert M. Gingrich and Christoph Adami in Physical Review Letters 89, 270402 (issue of 30 December 2002) – which might be achieved, according to this book, by warping space so it’s either a fraction of the 90 degrees allowing instantaneous travel or almost at 270 degrees to space as we know it. (shrink)

Abstract— According to studies, buildings use around 40% of the total energy consumption in the world. Most of this consumed energy comes from fossil fuel, one of the sources of environmental pollution. The Net Zero Energy Building (NZEB) is an alternative to this alarming pollution. With its reduced energy needs and renewable energy systems, a ZEB can return as much energy as it takes from the utility on an annual basis. Thus the main objective of this study is to discuss (...) the economical and friendly environmental renewable energy system integrated to building in Egypt to be (NZEB) economical by maximizing the renewable energy fraction and minimizing the greenhouse gases (GHG) emissions. The system consists of two renewable energy sources, comprising photovoltaic system, a wind turbine are considered for the proposed building under the study. By Utilizing the well-known Hybrid Optimization of Multiple Electric Renewables software to get the optimal configuration of a hybrid renewable energy system, based on the user inputs of loads, costs, technical details, solar and wind resources availability. (shrink)

Abstract: Hydrates are an enormous energy resource with global circulation in the permafrost and in the oceans. Even if conventional estimates are deliberated and only a small fraction is recoverable, the pure size of the resource is so huge that it demands assessment as a potential energy source. In this research work, we discuss the hydrate production prediction with Computer Modeling Group STARS (CMG STARS). In this paper different literatures reviews have been visited concerning hydrate production prediction with CMG STARS (...) and this have been done through consulting internet search in which secondary data were extracted. It was observed that most literatures does not quantify the knowledge on how hydrates production prediction with CMG STARS can be done. It was recommended that in the future, the research work on hydrate production prediction with CMG needs to be done by performing sensitivity analysis of different reservoir parameters which affect production process and commences the simulation model for the production prediction. (shrink)

A major question in sensory science is how a sensation of magnitude F (such as loudness) depends upon a sensory stimulus of physical intensity I (such as a sound-pressure-wave of root-mean-square sound-pressure-level). An empirical just-noticeable sensation difference (∆F)_j at F_j specifies a just-noticeable intensity difference (∆I)_j at I_j. Classically, intensity differences accumulate from a stimulus-detection threshold I_th up to a desired intensity I. The corresponding sensation differences likewise accumulate up to F(I) from F(I_th ), the non-zero sensation (as suggested by (...) hearing studies) at I_th. Consequently, sensation growth F(I) can be obtained through classic Fechnerian integration, in which some empirically-based relation for the Weber Fraction, ∆I⁄I, is combined with either Fechner’s Law ∆F=B or Ekman’s Law (∆F⁄F)=g. The number of steps in I is equated to the number of steps in F; an infinite series ensues, whose higher-order terms are traditionally ignored (Fechnerian integration). But also, remarkably, so are the integration bounds I_th and F(I_th ). Here, we depart from orthodoxy by including those bounds. Bounded Fechnerian integration is first used to derive hypothetical sensation-growth equations for which the differential ∆F(I)=F(I+∆I)-F(I) does indeed return either Fechner’s Law or Ekman’s Law respectively. One relation emerges: linear growth of sensation F with intensity I. Subsequently, 24 sensation-growth equations F(I) that the author had derived using bounded Fechnerian integration (12 equations for the Weber Fraction (∆I⁄I), each combined with either Fechner’s Law or with Ekman’s Law) are scrutinized for whether their differentials F(I+∆I)-F(I) return the respective Fechner’s Law or Ekman’s Law, particularly in the previously-unexamined limits (∆I⁄I)≪1 and (∆I⁄I)→0. Classic claims made by Luce and Edwards (1958) are then examined, viz., that three popular forms of the Weber Fraction, when combined with Fechner’s Law, produce sensation-magnitude equations that subsequently return the selfsame Fechner’s Law. When sensation-growth equations are derived here using bounded Fechnerian integration, Luce and Edwards (1958) prove to be wrong. (shrink)

This text is an English translation of those several sections of the original paper in Russian, where collection-related issues are considered. The full citation of the original paper is as following: Pavlinov I.Ya. 2016. [Bioraznoobrazie i biokollektsii: problema sootvetstvia]. In: Pavlinov I.Ya. (comp.). Aspects of Biodiversity. Archives of Zoological Museum of Lomonosov Moscow State University, Vol. 54, Pр. 733–786. -/- Orientation of biology, as a natural science, on the study and explanation of the similarities and differences between organisms led in (...) the second half of the 20th century to the recognition of a specifi c subject area of biological explorations, viz. biodiversity (BD). One of the important general scientifi c prerequisites for this shift was understanding that (at the level of ontology) the structured diversity of the living nature is its fundamental property equivocal to subjecting of some of its manifestations to certain laws. At the level of epistemology, this led to acknowledging that the “diversifi cationary” approach to description of the living beings is as justifi able as the before dominated “unifi cationary” one. This general trend has led to a signifi cant increase in the attention to BD. From a pragmatic perspective, its leitmotif was conservation of BD as a renewable resource, while from a scientifi c perspective the leitmotif was studying it was studying BD as a specifi c natural phenomenon. These two points of view are united by recognition of the need for scientific substantiation of BD conservation strategy, which implies the need for a detailed study of BD itself. At the level of ontology, one of the key problems in the study of BD (leaving aside the question of its genesis) is determination of its structure, which is interpreted as a manifestation of the structure of the Earth’s biota itself. With this, it is acknowledged that the subject area of empirical explorations is not the BD as a whole ( “Umgebung”) but its particular manifestations (“Umwelts”). It is proposed herewith to recognized, within the latter: fragments of BD (especially taxa and ecosystems), hierarchical levels of BD (primarily within- and interorganismal ones), and aspects of BD (before all taxonomic and meronomic ones). Attention is drawn to a new interpretation of bioinformatics as a discipline that studies the information support of BD explorations. An important fraction of this support are biocollections. The scientifi c value of collections means that they make it possible both empirical inferring and testing (verification) of the knowledge about BD. This makes biocollections, in their epistemological status, equivalent to experiments, and so makes studies of BD quite scientific. It is emphasized that the natural objects (naturalia), which are permanently kept in collections, contain primary (objective) information about BD, while information retrieved somehow from them is a secondary (subjective) one. Collection, as an information resource, serves as a research sample in the studies of BD. Collection pool, as the totality of all collection materials kept in repositories according to certain standards, can be treated as a general sample, and every single collection as a local sample. The main characteristic of collection-as-sample is its representativeness; so the basic strategy of development of the collection pool is to maximize its representativeness as a means to ensure correspondence of structure of biocollection pool to that of BD itself. The most fundamental characteristic of collection, as an information resource, is its scientific signifi cance. The following three main groups of more particular characteristics are distinguished: — the “proper” characteristics of every collection are its meaningfulness, informativeness, reliability, adequacy, documenting, systematicity, volume, structure, uniqueness, stability, lability; — the “external” characteristics of collection are resolution, usability, ethic constituent; — the “service” characteristics of collection are its museofication, storage system security, inclusion in metastructure, cost. In the contemporary world, development of the biocollection pool, as a specific resource for BD research, requires considerable organizational efforts, including work on their “information support” aimed at demonstrating the necessity of existence of the biocollections. (shrink)