Theory Of Multiplication Research Articles

At-power subcritical multiplication in the Advanced Test Reactor during nuclear requalification testing

Power division information during nuclear requalification of the Advanced Test Reactor (ATR) is of considerable interest as an importance function for observed changes to core reactivity. The degree to which a given physical subdivision of a critical reactor acts as a neutron source for other lobes is not analytically characterized for general application. When ATR operates at power, individual power-producing lobes rely on each other as neutron sources in order to maintain constant power, which in general requires either exactly critical multiplication within a reactor or an external neutron source. This work shows that fuel element and lobe powers in ATR can be related with subcritical multiplication theory. Subcritical multiplication factors are computed with a physically validated analytical method based on actual at-power operation, quantifying for each lobe its dependence on other lobes as an external neutron source. This explanation is significant for ATR due to the desire to irradiate a large variety of experiments simultaneously, each having its impact on the core neutron population. For any physical subdivision of any other critical reactor, it is likewise true that the subdivision undergoes only subcritical multiplication.

Gregor Mendel and the theory of species multiplication.

According to the revisionist interpretation of Mendel's pea crosses, his primary aim was not to study the inheritance of traits. Instead, he was interested in the question raised by Linnaeus as to whether new species could arise from the hybridization of existing species. The genetic interpretation is therefore seen as ahistorical by the revisionists. This view goes back to the 1979 article "Mendel no Mendelian?" by the historian of science R.C. Olby. A closer analysis shows that Olby implicitly assumed Mendel adhered to the unusual strictest species definition for Pisum. However, we argue that Mendel only mentions the hypothetical application of this strict definition in his 1866 paper. Like most of his contemporaries, Mendel accepted variation within species where the differences between varieties and species were a matter of degree. After researching variable hybrids in peas (Pisum; 1854-1863), Mendel also studied constant hybrids in hawkweeds (Hieracium; 1866-1873), which he considered to be new species. There is no debate about the latter, but the matter becomes muddled because Olby lumps Pisum and Hieracium together, despite their having completely different reproduction systems. Based on newly discovered historical sources, we also dispute several other assumptions made by Olby. We do not consider Olby's claim that Mendel conducted the Pisum experiments to investigate species multiplication to be tenable.

Differential analysis of the NBC algorithm based on mixed integer linear programming model

AbstractThis paper mainly studies mixed integer linear programming (MILP)‐based cryptanalysis on round‐reduced NBC algorithm with generalized Feistel structure. First, each component of the algorithm is equivalently described by linear inequality equations, and the propagation rules of differential characteristics and linear approximation are described, and an automatic search algorithm model of differential mode and linear mask mode based on MILP is established, and the minimum number of active S‐boxes and the corresponding differential mode and linear mask mode paths are obtained. Second, according to the NBC algorithm's 16‐bit block pull‐wire position permutation characteristics, the optimal full diffusion rounds of NBC‐128 algorithm and NBC‐256 algorithm are obtained by using approximate matrix multiplication theory to be six and eight respectively. Finally, based on the optimal number of full diffusion rounds of the algorithm, an automatic search algorithm model of impossible differential cryptanalysis is established, and the set of input differential patterns is traversed to obtain 11‐round impossible differential distinguishers of NBC‐128 algorithm and 14‐round impossible differential distinguishers of NBC‐256 algorithm respectively.

A Study on Electromagnetic Scattering Characteristics of 4-D Antenna Arrays

A theoretical study on electromagnetic scattering mechanism of 4-D antenna arrays is performed for the first time. First, the scattering fields of one antenna element within an infinite 4-D array are derived under periodic boundary conditions. In order to estimate the scattering performances of 4-D antenna arrays, numerical models of the scattering fields are then established based on the traditional scattering pattern multiplication theory. Moreover, an effective time-domain full-wave approach is proposed for the scattering cross section (SCS) simulation of 4-D arrays. Finally, to verify the feasibility for SCS reduction through 4-D arrays, the differential evolution (DE) algorithm is adopted to synthesize a 14-element microstrip patch antenna array for the optimization of radiation and scattering performances. Numerical results show that 4-D arrays are capable of scattering the incident waves in both space domain and frequency domain simultaneously, thus accomplishing remarkable in-band SCS reduction.

At-power subcritical multiplication in the advanced test reactor

The degree to which a given physical subdivision of a critical reactor acts as a neutron source for other lobes is not analytically characterized for general application. ATR and ATRC both operate at power, and individual power-producing lobes rely on each other as neutron sources in order to maintain constant power, which in general requires either exactly critical multiplication within a reactor or an external neutron source. This work shows that lobe powers in ATR or ATRC can be related with subcritical multiplication theory, demonstrating that the lobes are not individually critical. This explanation is significant for ATR due to the desire to irradiate a large variety of experiments simultaneously, each having its impact on the core neutron population. This work also establishes the lack of relationship between experiment reactivity worth and cross-sections calculated from fundamental nuclear data. For any physical subdivision of any other critical reactor, it is likewise true that the subdivision undergoes only subcritical multiplication.

Insight into the comprehensive effect of carbon dioxide, light intensity and glucose on heterotrophic-assisted phototrophic microalgae biofilm growth: A multifactorial kinetic model

Heterotrophic-assisted photoautotrophic microalgae biofilm cultivation was an alternative way to realize CO2 reduction and wastewater treatment. Growth kinetics supplied a channel to better understand how the cultivation conditions affect microalgal growth and CO2 reduction. However, the two growth modes (heterotroph and photoautotroph) have different needs for organic and inorganic nutrients. Thus, combining the threshold theory and multiplication theory, an integral multifactorial kinetic model that looking insight into the comprehensive effect of glucose, CO2, light intensity, and nitrate was developed for heterotrophic-assisted photoautotrophic microalgae biofilm growth in this study. R2 between model and experiment was 0.99. It predicted the maximum specific growth rate and maximum CO2 consumption rate of heterotrophic-assisted photoautotrophic microalgae biofilm was 1.868 h−1 and 1.02 h−1, respectively. This model fully explained the influence of the main factors on microalgae biofilm growth and reasonably predicted the growth rate of microalgae biofilm under different growth conditions.

Legendre’s Singular Modulus

In 1811, Legendre published an identity between integrals involving the constant that inspired Abel to create his brilliant theory of complex multiplication. Then k reappeared as the eccentricity of an ellipse whose arclength Ramanujan computed explicitly in terms of gamma functions with rational arguments. Finally, the constant appeared as a consequence of the three-body choreography along Bernoulli’s lemniscate. We develop these results in detail as well as mentioning random walks on a cubic lattice and the renormalization of the period of the simple pendulum. All this shows the wonderful unity underlying seemingly different branches of mathematics and physics.

The Galois action on symplectic K-theory

We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of {mathbf {Q}}. We compute this action explicitly. The representations we see are extensions of Tate twists {mathbf {Z}}_p(2k-1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.

The δ′ wave solution to a totally degenerate system of conservation laws

We focus on the Riemann solutions to a totally degenerate system of conservation laws with repeated eigenvalues and repeated eigenvectors. Based on the theory of multiplication of distributions, we define α-solution to this system within a convenient space of distributions, and then establish both the expressions of the α-solutions and the condition of occurrence of each α-solution to this system. With these results, we solve the Riemann problem and then obtain all of exact solutions which are independent of α. It is shown that the delta wave issues in the solution. It is also noticed that both the delta wave and the vacuum state arise simultaneously in the solution. Moreover, the δ′ wave emerges in the solution. Finally, the exact solutions agree with the corresponding numerical solutions.

Challenge Problems for a Theory of Degree Multiplication (with partial answer key)

This paper offers a theory of degree multiplication in natural language semantics. Motivation for the development such a theory comes from proportional readings of quantity words and rate expressions such as miles per hour. After laying out a set of ‘challenge problems’ that any good theory of degree multiplication should be able to handle, I set about solving them, borrowing mathematical tools from quantity calculus. These algebraic foundations are integrated into a compositional Montagovian framework, yielding a system that can solve, or partially solve, some of the problems.

Алгебры бинарных изолирующих формул для теорий тензорных произведений

Algebras of distributions of binary isolating and semi-isolating formulae are derived objects for a given theory and reflect binary formula relations between 1-type realizations. These algebras are related to the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to theories from that class, and classify those algebras; 2) classify theories from the class according to the isolating and semi-isolating formulae algebras defined by those theories. The description of a finite algebra of binary isolating formulas unambiguously implies the description of an algebra of binary semi-isolating formulas, which makes it possible to trace the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulas for tensor products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems are formulated describing all algebras of binary formulae distributions for tensor multiplication theory of regular polygons on an edge. It is shown that they are completely described by two algebras

Interactions between parental and personal socioeconomic resources and self-rated health: Adjudicating between the resource substitution and resource multiplication theories

A small body of research has documented intriguing findings, mostly from the United States but also from Europe, which suggest that the positive health effects of socioeconomic resources in adulthood may be conditioned by socioeconomic circumstances in childhood. There are two competing theories in this literature. The first contends that socioeconomic resources have a stronger effect on adult health for people from disadvantaged backgrounds because socioeconomic resources in adulthood substitute or compensate for a paucity of health-related resources earlier in life. The second contends that socioeconomic resources have a stronger effect on adult health for people from advantaged backgrounds because socioeconomic resources in adulthood compound or multiply the health effects of socioeconomic resources earlier in life. We used survey data from the 2012 Longitudinal and International Study of Adults linked to current and historical income data from the Canada Revenue Agency to investigate interactions between parental and personal socioeconomic resources – education and income, treated separately – as predictors of self-rated health in a sample of Canadians aged 25 to 50. Consistent with the resource multiplication theory, we found that the presumed benefits of personal family income for self-rated health were stronger for women from wealthier backgrounds than for women from poorer backgrounds. We found no evidence to support either theory among men. Overall, none of the interactions involving the education of parents or their adult children reached statistical significance. Our results are indicative of the importance of distinguishing between education and income for adults and their parents when adjudicating between these two theories.

Development of an Educational Code of Deriving Equations of Motion and Analyzing Dynamic Characteristics of Multibody Closed Chain Systems using GNU Octave for a Beginner

In this study, an automatic GNU Octave code, a free high-level language, for the educational purposes was developed to derive equations of motion and constrain equations of a multibody closed chain system and to calculate the response of the system. The code for calculating the dynamic response was developed by formulating several equations in symbolic expression and extracting differential-algebraic equations in matrix form. The code has a similar structure to the previous code for the open chained system, but it deals with the constraint equation and different numerical integration. The examples of closed chain systems provide an additional procedure to derive the constraint equations by using Lagrangian multiplication theory and to solve the differential-algebraic equations using the Runge-Kutta method. The code was made to understand the theory of analysis and the structure of calculation easily. In addition, the code has an automatic process of the derivation of the Lagrange equation and the constraint equations in matrix form after inputting the number of symbolic information such as position and velocity coordinates and design variables of the system that the user wants to review. The code was validated by comparing the dynamic response of the four-bar linkage with the same design variables and initial conditions of the previous work. By using the code, the reader's ability to exchange information such as symbols and matrices will be expected to be improved.

Multi-Damage Identification of Multi-Span Bridges Based on Influence Lines

The framework security of a bridge is essential as a critical component of traffic engineering. Even though the bridge structure is damaged to various degrees due to various reasons, the bridge will be wrecked when the damage reaches a particular level, suggesting a negative influence on people’s lives. Based on the current situation and existing problems of structural damage identification of bridges, a structural damage identification technology of continuous beam bridges based on deflection influence lines is proposed in this paper in order to keep track of and always detect broken bridge elements, thereby extending the bridge’s service life and reducing the risk of catastrophic accidents. The line function expression of deflection impact on a multi-span continuous beam bridge was first obtained using Graphic Multiplication theory. From the theoretical level, the influence line function of the continuous beam bridge without extensive damage was computed, and a graph was generated. The photographs of the DIL as well as the first and second derivatives, the deflection influence line distinction and its first and second derivatives, and the DIL distinction and its first and second derivatives of a continuous beam bridge in a single position and multi-position destruction were fitted in this paper. Finally, after comparing multiple work conditions and multiple measuring points, it was found that the first derivative of deflection influence line difference had the best damage identification effect. The design was completed and tested, which had verified the feasibility of this theory.

Pengaruh Metode Jartik (Jarimatika) dalam Pembelajaran Daring Terhadap Hasil Belajar Perkalian Siswa Kelas II Sekolah Dasar

The low numeracy ability of student in elementary schools is focus problem in this study, particularly on multiplication theory during online learning. In addition, the inadequate use of methods in online multiplication learning has resulted in low student. This study aimed to determine the distinctions in the multiplication learning result of grade 2nd elementary school student after using Jarimatika method in online learning. This study is a quantitative with the experimental method by control group design. The number of samples is 20 students of class 2 A as the experimental group and 20 students of class 2 B as the control group. Tests and observations are the data collections technique is used. Based on the result of the hypothesis test by the Man Whitney test with the SPSS version 25 application, Sig value is obtained. (2-tailed) 0.165 0.05. This value states that the result of null hypothesis (H0) proposed by the researcher are accepted and the alternative hypothesis (H1) is rejected. It means that is no distinction in multiplication learning result of grade 2nd elementary school students who use the Jarimatika method in online learning even though there is improvement in students’ scores.

Nonlinear terahertz effects of gold nanofilms

Nonlinear interaction between strong-field terahertz electromagnetic waves and matters will become one of the next hot research frontiers in nonlinear optics. However, the lack of strong terahertz radiation sources and appropriate nonlinear terahertz materials have impeded its progress. Here we systematically have investigated the strong-field terahertz nonlinear effects of gold (Au) nanofilms on different substrates, including SiO2, high-resistivity Si and SiO2-high-resistivity Si hybrid substrates. The strong-field terahertz waves are emitted from lithium niobate crystals via tilted pulse front technique, and obvious nonlinear transmission responses are observed along with varying the incident field strengths for all the Au samples on the three types of the substrates. The nonlinear behavior is enhanced when the gold nanofilm thickness increases, which can be qualitatively understood by introducing the quantum tunneling effect and carrier multiplication theory generated at the Au nano-slits under the illumination of the strong-field terahertz pulses. Our demonstrations not only open a new paradigm for nonlinear terahertz investigations and future high-speed terahertz devices, but also provide an effective platform for exploring extreme terahertz sciences.

A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

Motivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in {mathbb {R}}^{n} and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than {mathbb {Z}}^{*}={mathbb {Z}}{setminus }{0}) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

Алгебры бинарных изолирующих формул для теорий корневых произведений графов

Algebras of distributions of binary isolating and semi-isolating formulas are derived objects for given theory and reflect binary formula relations between realizations of 1-types. These algebras are associated with the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to the theories from this class and classify these algebras; 2) to classify theories from a given class depending on the algebras defined by these theories of isolating and semi-isolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semi-isolating formulas, which makes it possible to track the behavior of all binary formula relations of a given theory. The paper describes algebras of binary formulae for root products. The Cayley tables are given for the obtained algebras. Based on these tables, theorems describing all algebras of binary formulae distributions for the root multiplication theory of regular polygons on an edge are formulated. It is shown that they are completely described by two algebras.

Effect of scratch defects on photoinduced damage characteristics of fused quartz

When a laser beam irradiates an optical material, a light standing wave field should be observed inside the optical material due to the interference between the beam reflected from the rear surface and the incident beam. If there are scratches on the surface, the incident light can be modulated and the distribution of the standing wave field inside the material is not uniform any more. Therefore, the appearance of the local enhancement of light will change the damage characteristics of optical material. To analyze the field damage characteristics of optical material with scratches, a theoretical analysis model is established. It can be used to study the damage characteristics and build a priori model of actual optical material. Fused quartz is employed as the study object, and the modulation effect of defect on light field is simulated by finite difference time domain (FDTD). Based on the electron multiplication theory, the effect of the number and the positions of scratches on the damage characteristics of fused quartz are calculated in detail. The results show that the phase modulation of the scratch will destroy the uniformity of the standing wave field when the scratch defect material is irradiated by laser. Due to the influence of the standing wave field, the maximum field intensity appears near the rear surface of the material, which explains the phenomenon that the rear surface of the material is more prone to damage points. When there are multiple scratches on the material surface, the distribution of light field is related to the number of the scratches. Specifically, the maximum field intensity increases with the number of scratches increasing. Taking fused quartz material for example, when a 10-ps pulse is incident on it, if three scratches are located on its surface, then the modulation effect on the light field is strongest, and the damage threshold is 66.1% lower than that of the ideal material. In addition, the scratch spacing also has an effect on the standing wave field and field damage characteristics of the material, and the specific effect of the interval can be analyzed directly by using the calculation model proposed in this paper.

Diagonal restrictions of p-adic Eisenstein families

We compute the diagonal restriction of the first derivative with respect to the weight of a p-adic family of Hilbert modular Eisenstein series attached to a general (odd) character of the narrow class group of a real quadratic field, and express the Fourier coefficients of its ordinary projection in terms of the values of a distinguished rigid analytic cocycle in the sense of Darmon and Vonk (Duke Math J, to appear, 2020) at appropriate real quadratic points of Drinfeld’s p-adic upper half-plane. This can be viewed as the p-adic counterpart of a seminal calculation of Gross and Zagier (J Reine Angew Math 355:191–220, 1985, §7) which arose in their “analytic proof” of the factorisation of differences of singular moduli, and whose inspiration can be traced to Siegel’s proof of the rationality of the values at negative integers of the Dedekind zeta function of a totally real field. Our main identity enriches the dictionary between the classical theory of complex multiplication and its extension to real quadratic fields based on RM values of rigid meromorphic cocycles, and leads to an expression for the p-adic logarithms of Gross–Stark units and Stark–Heegner points in terms of the first derivatives of certain twisted Rankin triple product p-adic L-functions.