Search results for: Caputo fractional derivative

Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favorable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. Psychology research has demonstrated that positive comprehension becomes possible when new information becomes part of student’s subjective experience and when linkages between the attributes of notions and various ways of their presentations can be established. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. The article describes the implementation of a holistic approach to teaching mathematics designed to address the primary challenges of such teaching, specifically, the challenge of students’ comprehension. This approach consists of (1) establishing links between the attributes of a notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience -emotional and value, contextual, procedural, communicative- during the educational process; (3) links between different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modeling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and technology influence understanding of material used in teaching mathematics was the research’s primary goal. The research included an experiment in which 256 secondary school students took part: 142 in the experimental group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics -'Derivative' and 'Trigonometric functions'- was evaluated. Control group participants were taught using traditional methods. Students in the experimental group were taught using the holistic method: under the teacher’s guidance, they carried out problems designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as problems that required the ability to operate with all modes of presentation. The use of the technology that forms inter-subject notions based on linkages between perceptional, real, and conceptual mathematical spaces proved to be of special interest to the students. Results of the experiment were analyzed by presenting students in each of the groups with a final test in each of the studied topics. The test included problems that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion was used to reveal the statistical significance of results (pass-fail the modeling test). A significant difference in results was revealed (p < 0.001), which allowed the authors to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. Also, it was revealed (used Student’s t-test) that the students of the experimental group performed reliably (p = 0.0001) more problems in comparison with those in the control group. The results obtained allow us to conclude that increasing comprehension and assimilation of study material took place as a result of applying implemented methods and techniques.

Keywords: comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions

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Authors: Vishal Kumar, Soumitra Satapathi

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Föster Resonance Energy Transfer (FRET) is a powerful technique used to probe close-range molecular interactions. Physically, the FRET phenomenon manifests as a dipole–dipole interaction between closely juxtaposed fluorescent molecules (10–100 Å). Our effort is to employ this FRET technique to make a prototype device for highly sensitive detection of environment pollutant. Among the most common environmental pollutants, nitroaromatic compounds (NACs) are of particular interest because of their durability and toxicity. That’s why, sensitive and selective detection of small amounts of nitroaromatic explosives, in particular, 2,4,6-trinitrophenol (TNP), 2,4-dinitrotoluene (DNT) and 2,4,6-trinitrotoluene (TNT) has been a critical challenge due to the increasing threat of explosive-based terrorism and the need of environmental monitoring of drinking and waste water. In addition, the excessive utilization of TNP in several other areas such as burn ointment, pesticides, glass and the leather industry resulted in environmental accumulation, and is eventually contaminating the soil and aquatic systems. To the date, high number of elegant methods, including fluorimetry, gas chromatography, mass, ion-mobility and Raman spectrometry have been successfully applied for explosive detection. Among these efforts, fluorescence-quenching methods based on the mechanism of FRET show good assembly flexibility, high selectivity and sensitivity. Here, we report a FRET-based sensor system for the highly selective detection of NACs, such as TNP, DNT and TNT. The sensor system is composed of a copolymer Poly [(N,N-dimethylacrylamide)-co-(Boc-Trp-EMA)] (RP) bearing tryptophan derivative in the side chain as donor and dansyl tagged copolymer P(MMA-co-Dansyl-Ala-HEMA) (DCP) as an acceptor. Initially, the inherent fluorescence of RP copolymer is quenched by non-radiative energy transfer to DCP which only happens once the two molecules are within Förster critical distance (R0). The excellent spectral overlap (Jλ= 6.08×10¹⁴ nm⁴M⁻¹cm⁻¹) between donors’ (RP) emission profile and acceptors’ (DCP) absorption profile makes them an exciting and efficient FRET pair i.e. further confirmed by the high rate of energy transfer from RP to DCP i.e. 0.87 ns⁻¹ and lifetime measurement by time correlated single photon counting (TCSPC) to validate the 64% FRET efficiency. This FRET pair exhibited a specific fluorescence response to NACs such as DNT, TNT and TNP with 5.4, 2.3 and 0.4 µM LODs, respectively. The detection of NACs occurs with high sensitivity by photoluminescence quenching of FRET signal induced by photo-induced electron transfer (PET) from electron-rich FRET pair to electron-deficient NAC molecules. The estimated stern-volmer constant (KSV) values for DNT, TNT and TNP are 6.9 × 10³, 7.0 × 10³ and 1.6 × 104 M⁻¹, respectively. The mechanistic details of molecular interactions are established by time-resolved fluorescence, steady-state fluorescence and absorption spectroscopy confirmed that the sensing process is of mixed type, i.e. both dynamic and static quenching as lifetime of FRET system (0.73 ns) is reduced to 0.55, 0.57 and 0.61 ns DNT, TNT and TNP, respectively. In summary, the simplicity and sensitivity of this novel FRET sensor opens up the possibility of designing optical sensor of various NACs in one single platform for developing multimodal sensor for environmental monitoring and future field based study.

Keywords: FRET, nitroaromatic, stern-Volmer constant, tryptophan and dansyl tagged copolymer

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Authors: Shuai Yuan, Minxia Shi, Xu Zhang, Jianzhi Yang, Kangqi Tian, Yuzheng Ma

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The precise measurement of muscle activities is essential for understanding the function of various body movements. This work aims to develop a muscle magnetic field signal detection system based on mathematical analysis. Medical research has underscored that early detection of muscle atrophy, coupled with lifestyle adjustments such as dietary control and increased exercise, can significantly enhance muscle-related diseases. Currently, surface electromyography (sEMG) is widely employed in research as an early predictor of muscle atrophy. Nonetheless, the primary limitation of using sEMG to forecast muscle strength is its inability to directly measure the signals generated by muscles. Challenges arise from potential skin-electrode contact issues due to perspiration, leading to inaccurate signals or even signal loss. Additionally, resistance and phase are significantly impacted by adipose layers. The recent emergence of optically pumped magnetometers introduces a fresh avenue for bio-magnetic field measurement techniques. These magnetometers possess high sensitivity and obviate the need for a cryogenic environment unlike superconducting quantum interference devices (SQUIDs). They detect muscle magnetic field signals in the range of tens to thousands of femtoteslas (fT). The utilization of magnetometers for capturing muscle magnetic field signals remains unaffected by issues of perspiration and adipose layers. Since their introduction, optically pumped atomic magnetometers have found extensive application in exploring the magnetic fields of organs such as cardiac and brain magnetism. The optimal operation of these magnetometers necessitates an environment with an ultra-weak magnetic field. To achieve such an environment, researchers usually utilize a combination of active magnetic compensation technology with passive magnetic shielding technology. Passive magnetic shielding technology uses a magnetic shielding device built with high permeability materials to attenuate the external magnetic field to a few nT. Compared with more layers, the coils that can generate a reverse magnetic field to precisely compensate for the residual magnetic fields are cheaper and more flexible. To attain even lower magnetic fields, compensation coils designed by Biot-Savart law are involved to generate a counteractive magnetic field to eliminate residual magnetic fields. By solving the magnetic field expression of discrete points in the target region, the parameters that determine the current density distribution on the plane can be obtained through the conventional target field method. The current density is obtained from the partial derivative of the stream function, which can be represented by the combination of trigonometric functions. Optimization algorithms in mathematics are introduced into coil design to obtain the optimal current density distribution. A one-dimensional linear regression analysis was performed on the collected data, obtaining a coefficient of determination R2 of 0.9349 with a p-value of 0. This statistical result indicates a stable relationship between the peak-to-peak value (PPV) of the muscle magnetic field signal and the magnitude of grip strength. This system is expected to be a widely used tool for healthcare professionals to gain deeper insights into the muscle health of their patients.

Keywords: muscle magnetic signal, magnetic shielding, compensation coils, trigonometric functions.

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Authors: Nathan Garcia

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The polarizing dialogue of contemporary political America results from core philosophical differences. But these differences are beyond ideological and reach metaphysical distinction. Good intellectual historians have theorized that fundamental concepts such as freedom, God, and nature have been sterilized of their intellectual vigor. They are partially correct. 19th-century pragmatist Charles Sanders Peirce offers a penetrating philosophy which can yield greater insight into the contemporary political divide. Peirce argues that metaphysical and ethical issues are derivative of operational logic. His triadic logical structure and ensuing metaphysical principles constructed therefrom is contemporaneously applicable for three reasons. First, Peirce’s logic aptly scrutinizes the logical processes of liberal and conservative mindsets. Each group arrives at a cosmological root metaphor (abduction), resulting in a contemporary assessment (deduction), ultimately prompting attempts to verify the original abduction (induction). Peirce’s system demonstrates that liberal citizens develop a cosmological root metaphor in the concept of fairness (abduction), resulting in a contemporary assessment of, for example, underrepresented communities being unfairly preyed upon (deduction), thereby inciting anger toward traditional socio-political structures suspected of purposefully destabilizing minority communities (induction). Similarly, conservative citizens develop a cosmological root metaphor in the concept of freedom (abduction), resulting in a contemporary assessment of, for example, liberal citizens advocating an expansion of governmental powers (deduction), thereby inciting anger towards liberal communities suspected of attacking freedoms of ordinary Americans in a bid to empower their interests through the government (induction). The value of this triadic assessment is the categorization of distinct types of inferential logic by their purpose and boundaries. Only deductive claims can be concretely proven, while abductive claims are merely preliminary hypotheses, and inductive claims are accountable to interdisciplinary oversight. Liberals and conservative logical processes preclude constructive dialogue because of (a) an unshared abductive framework, and (b) misunderstanding the rules and responsibilities of their types of claims. Second, Peircean metaphysical principles offer a greater summary of the contemporaneously divisive political climate. His insights can weed through the partisan theorizing to unravel the underlying philosophical problems. Corrosive nominalistic and essentialistic presuppositions weaken the ability to share experiences and communicate effectively, both requisite for any promising constructive dialogue. Peirce’s pragmatist system can expose and evade fallacious thinking in pursuit of a refreshing alternative framework. Finally, Peirce’s metaphysical foundation enables a logically coherent, scientifically informed orthopraxis well-suited for American dialogue. His logical structure necessitates radically different anthropology conducive to shared experiences and dialogue within a dynamic, cultural continuum. Pierce’s fallibilism and sensitivity to religious sentiment successfully navigate between liberal and conservative values. In sum, he provides a normative paradigm for intranational dialogue that privileges individual experience and values morally defensible notions of freedom, God, and nature. Utilizing Peirce’s thought will yield fruitful analysis and offers a promising philosophical alternative for framing and engaging in contemporary American political discourse.

Keywords: Charles s. Peirce, american politics, logic, pragmatism

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Authors: P. C. Kutschera, Elena C. Tesoro, Mary Grace Talamera-Sandico, Jose Maria G. Pelayo III

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Second generation military Filipino Amerasians comprise a formidable contemporary segment of the estimated 250,000-plus biracial Amerasians in the Philippines today. Overall, they are a stigmatized and socioeconomically marginalized diaspora, historically; they were abandoned or estranged by U.S. military personnel fathers assigned during the century-long Colonial, Post-World War II and Cold War Era of permanent military basing (1898-1992). Indeed, U.S. military personnel remain stationed in smaller numbers in the Philippines today. This inquiry is an outgrowth of two recent small sample studies. The first surfaced the impact of the U.S. military prostitution system on formation of the ‘Derivative Amerasian Family Construct’ on first generation Amerasians; a second, qualitative case study suggested the continued effect of the prostitution systems' destructive impetuous on second generation Amerasians. The intent of this current qualitative, multiple-case study was to actively seek out second generation sex industry toilers. The purpose was to focus further on this human phenomenon in the post-basing and post-military prostitution system eras. As background, the former military prostitution apparatus has transformed into a modern dynamic of rampant sex tourism and prostitution nationwide. This is characterized by hotel and resorts offering unrestricted carnal access, urban and provincial brothels (casas), discos, bars and pickup clubs, massage parlors, local barrio karaoke bars and street prostitution. A small case study sample (N = 4) of female and male second generation Amerasians were selected. Sample formation employed a non-probability ‘snowball’ technique drawing respondents from the notorious Angeles, Metro Manila, Olongapo City ‘AMO Amerasian Triangle’ where most former U.S. military installations were sited and modern sex tourism thrives. A six-month study and analysis of in-depth interviews of female and male sex laborers, their families and peers revealed a litany of disturbing, and troublesome experiences. Results showed profiles of debilitating human poverty, history of family disorganization, stigmatization, social marginalization and the ghost of the military prostitution system and its harmful legacy on Amerasian family units. Emerging were testimonials of wayward young people ensnared in a maelstrom of deep economic deprivation, familial dysfunction, psychological desperation and societal indifference. The paper recommends that more study is needed and implications of unstudied psychosocial and socioeconomic experiences of distressed younger generations of military Amerasians require specific research. Heretofore apathetic or disengaged U.S. institutions need to confront the issue and formulate activist and solution-oriented social welfare, human services and immigration easement policies and alternatives. These institutions specifically include academic and social science research agencies, corporate foundations, the U.S. Congress, and Departments of State, Defense and Health and Human Services, and Homeland Security (i.e. Citizen and Immigration Services) It is them who continue to endorse a laissez-faire policy of non-involvement over the entire Filipino Amerasian question. Such apathy, the paper concludes, relegates this consequential but neglected blood progeny to the status of humiliating destitution and exploitation. Amerasians; thus, remain entrapped in their former colonial, and neo-colonial habitat. Ironically, they are unwitting victims of a U.S. American homeland that fancies itself geo-politically as a strong and strategic military treaty ally of the Philippines in the Western Pacific.

Keywords: Asian Americans, diaspora, Filipino Amerasians, military prostitution, stigmatization

Procedia PDF Downloads 456