Order Coefficients Research Articles

Time-dependent lowest term estimation in a 2D bioheat transfer problem with nonlocal and convective boundary conditions

ABSTRACT A solution method for an inverse problem of determining the time-dependent lowest order coefficient of the 2D bioheat Pennes equation with nonlocal boundary conditions and total energy integral overdetermination condition recently appeared in literature is analysed and improved. Improvements include convective boundary condition into the model, the development of an accurate forward solver, accurate determination of total energy, and the proposal of a method for the numerical treatment of the inverse problem from noisy data. In the method, the 2D bioheat Pennes equation is solved by the method of lines based on a highly accurate pseudospectral approach, and sought coefficient values are estimated by the Levenberg–Marquardt method with the discrepancy principle as stopping rule. Numerical experiments are reported to illustrate effectiveness of the proposed method.

Mass measurements for the Tz=−2fp -shell nuclei Ti40 , Cr44 , Mn46 , Fe48 , Co50 , and Ni52

By using isochronous mass spectrometry (IMS) at the experimental cooler storage ring CSRe, masses of short-lived $^{44}$Cr, $^{46}$Mn, $^{48}$Fe, $^{50}$Co and $^{52}$Ni were measured for the first time and the precision of the mass of $^{40}$Ti was improved by a factor of about 2. Relative precisions of $\delta m/m=(1-2)\times$10$^{-6}$ have been achieved. Details of the measurements and data analysis are described. The obtained masses are compared with the Atomic-Mass Evaluation 2016 (AME$^{\prime}$16) and with theoretical model predictions. The new mass data enable us to extract the higher order coefficients, $d$ and $e$, of the quartic form of the isobaric multiplet mass equation (IMME) for the $fp$-shell isospin quintets. Unexpectedly large $d$- and $e$-values for $A=44$ quintet are found. By re-visiting the previous experimental data on $\beta$-delayed protons from $^{44}$Cr decay, it is suggested that the observed anomaly could be due to the misidentification of the $T=2$, $J^\pi=0^{+}$ isobaric analog state (IAS) in $^{44}$V.

Computing Group Velocities and Group-Velocity Dispersions of Optical Fibers Through Automatic Differentiation of Explicit Forms of Propagation Constants

We present a method to compute differential coefficients of the first and second orders, for propagation constants of nondegenerate and degenerate modes, propagating in an optical fiber to calculate dispersion characteristics of group velocities (GV) and group-velocity dispersions (GVD). This method automatically differentiates explicit forms of eigenvalues extracted from determinants of a generalized eigenvalue problem. This problem is converted from a nonlinear eigenvalue problem derived from the Trefftz method (e.g., transfer matrix and multipole methods) by the Sakurai-Sugiura method. We compute the differential coefficients of the second order of degenerate modes without computing eigenvectors and their first order differential coefficients in the generalized eigenvalue problems. Therefore, in parametric optimization, we can compute the differential coefficients of all propagating modes without remodeling the waveguide cross-section, as analyzing the whole cross-section avoids the symmetric conditions derived from the numerical model. Computed results with the proposed method for step-index and holey fibers validate the method and its effectiveness. In particular, our results show that our method computes the GV and GVD more accurately than computation using numerical differentiation.

Virial expansions, finite differences, and recursion relations

A general density expansion method based on the calculus of finite differences (Ramshaw J. D., J. Chem. Phys., 57 (1972) 2070) is revisited and reformulated. The original expression for the coefficients in the expansion is transformed into an alternative equivalent form which simplifies and facilitates their evaluation. The use of the method is illustrated by determining the virial coefficients of arbitrary order in a density expansion of the pressure in a classical monatomic gas. The resulting virial coefficients are expressed in terms of the Ursell reducible cluster integrals. The functional form of those expressions is determined by simple recursion relations.

Discrimination of seismic waves produced by volcanoes using self-organizing maps

The analysis and classification of seismic records of volcanoes allow us to determine the alert state in which it is. A timely study of these signs can contribute to decision-making to safeguard the integrity of people in the face of a natural disaster. The present work applies a methodology that combines the analysis of linear prediction coefficients and artificial neural networks to classify earthquakes. Two types of earthquakes that come from Galeras Volcano, Colombia, are studied volcano-tectonic and long-period. The classification is made using the clustering technique based on unsupervised learning. The signals are transformed using the linear prediction filter coefficients technique, which has the function of reducing the size of the vector that contains the original data. MATLAB software is used to generate a self-organizing network that handles clustering. The results show that the best alternative in unsupervised learning is to use the linear prediction coefficients of order 5, 6, and 7 to represent a seismic signal. For lower orders, the necessary information is not captured and for higher orders, noise information is shown.

Language Learning Styles and Writing Strategies as Predictors of Writing Anxiety among Iranian EFL Learners

The main aim of this study was to see if a significant relationship existed among Iranian EFL learners’ Learning Styles, Writing Strategies and Writing Anxiety. To this effect, 183 EFL learners studying English in three language institutes from the upper intermediate and advanced proficiency levels were selected based on convenient nonrandom sampling procedure. They completed the Kolb Learning Style (KLS), the Inventory of Learning Strategies for writing (ILS) and the Foreign Language Writing Anxiety Scale (FLWAS) self-report questionnaires. However, after the initial screening, 21 cases were discarded as their answers were incomplete, leaving 162 participants in the final sample. The relationship among EFL learners learning styles, writing strategies and writing anxiety were analyzed using the Spearman rank order coefficient of correlation. Since, the results indicated statistically significant relationships among them, multiple regression analyses were run to see if significant predictors of EFL learners’ writing anxiety could be identified. Interestingly, the analyses showed that pragmatist learning style made the strongest statistically significant unique contribution to predict writing anxiety while activist learning style failed to make such a significant contribution. To clarify, the negative relationship suggests that the more pragmatic the preferred learning style is, the lower the writing anxiety. Furthermore, only memory writing strategy made a statistically significant unique contribution to predicting writing anxiety while the other five writing strategies did not. To explain further, their positive relationship implies that learners who apply memory strategies more, face higher levels of writing anxiety. Thus, this study identified learners’ pragmatist learning style and memory writing strategy as significant predictors of writing anxiety in the EFL context. As a result, not only does this study provide statistical evidence of the relationship among these variables but it also stresses the importance of EFL learners’ language learning styles and writing strategies to their writing anxiety.

Correlation Power Analysis of KASUMI and Power Resilience Analysis of Some Equivalence Classes of KASUMI S-Boxes

The KASUMI block cipher imparts confidentiality and integrity to the 3G mobile communication systems. In this paper, we present power analysis attack on KASUMI as a two-pronged attack: first, the FL function is targeted, and subsequently the recovered output of FL function is used to mount attack on 7 × 7 and 9 × 9 S-boxes embedded in the FO function of the cipher. Our attack recovers all 128 bits of the secret key of KASUMI. Furthermore, we present a countermeasure for this attack which requires lesser resource footprint as compared with existing countermeasures, rendering such implementations practically feasible for resource-constrained applications, such as IoT and RFID devices. In addition, we propose linear equivalent mappings and Permutation-XOR equivalent mappings of 7 × 7 S-boxes which have stronger resilience against power analysis attacks with respect to the improved transparency order and confusion coefficient parameters while restoring the classical cryptographic properties. We point out some properties of linear equivalence (LE) classes of these S-boxes with respect to these metrics as well.

Hyperbolic Equations with Unknown Coefficients

We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness theorems for regular solutions are proved (i.e., for solutions having all weak derivatives in the sense of Sobolev, occuring in the equation).

Inverse Problem of Determining the Absorption Coefficient in a Degenerate Parabolic Equation in the Class of L2-Functions

We study the unique solvability of the inverse problem of determining the time-dependent lower order coefficient in a degenerate parabolic equation with one spatial variable under an additional integral observation condition. The unknown absorption coefficient is sought in the space L2(0, T). We prove the time-local existence and global uniqueness of a solution to the inverse problem.

Week-long protocol to monitor physical activity intensity and impact loading in children

Natural ankle quasi-stiffness (NAS) is a key metric used to personalize orthotic and prosthetic ankle-foot devices. NAS has traditionally been defined as the average slope (i.e. linear regression) of the net ankle moment vs. ankle angle curve during stance. However, NAS appears to have nonlinear characteristics. Characterizing nonlinear NAS across a wide range of tasks will enable us to incorporate these attributes into future orthotic and prosthetic ankle-foot device designs.Does nonlinear NAS change across multiple intensities of walking, running, and load carriage tasks?This observational study examined 22 young, healthy individuals as they walked, ran, and walked while carrying a load at three intensities (speed or load). Linear, quadratic, and cubic regressions were done on the net ankle moment vs. ankle angle curve over three phases of stance: impact, loading, and push-off. RMSE between regressions and measured data were computed to determine regression accuracy, and multilevel linear models (MLMs) were used to determine significant differences between coefficients across intensities.Quadratic and cubic regressions of NAS had significantly lower RMSE than linear NAS for all phases of stance. Because of diminishing reductions in RMSE between quadratic and cubic regressions, only quadratic regression coefficients were further analyzed. Most first (linear) and second (nonlinear) order coefficients of quadratic regressions exhibited clear trends with respect to changes in walking or running speed, but not to increases in load.This was the first study to our knowledge to thoroughly characterize nonlinear NAS across multiple gait tasks and intensities. This study provides an advanced understanding of the characteristics of nonlinear NAS for the design of future prosthetic and orthotic ankle-foot devices.

Scattering from a grounded chiral slab with rough interface using perturbation theory

Scattering from a grounded chiral slab with rough interface is studied using perturbation theory. A system of equations for zeroth and higher order solution is written, which can be solved to get co and cross polarized scattered and transmitted field components. The zeroth-order coefficients provide the results for the flat case, while the higher order coefficients provide the solution with perturbation involved. Upon substituting the value of chirality of the medium to zero, we get the results for the dielectric slab to highlight the effect of chirality. Moreover, the parameters related to sinusoidal and Gaussian rough surfaces such as period and correlation length are changed to check their effects on the scattering pattern.

Solidification of radioactive waste in lignite slag and bismuth oxide filled elastomer matrices: Release mechanism, immobilization efficiency, long term radiation stability and aging

This paper presents results of the experimental studies on immobilization of radioactive waste in composite elastomeric matrices based on the natural rubber and mineral fillers lignite slag and bismuth oxide. For preparation of the matrices a classical mixing procedure using a roll mill was applied using isotopically labeled fillers with adsorbed Cs-137, Co-60, Sr-90 and Am-241 tracers, followed by vulcanization at 160 °C and 20 MPa pressure. The composites were verified towards efficiency of radioactive isotopes immobilization and resistance against high radiation doses up to 1000 kGy. For this purpose such parameters as diffusion coefficients, leachability indexes, leaching rates as well as mechanical and radiation shielding properties for the native and radiation modified composites were determined and analyzed. The results proved very good immobilization efficiency of the waste bearing matrices and moderate radiation resistance. The results obtained from leaching experiments show effective diffusion coefficients of order 10−13–10−11 cm2·s−1, leachability indexes significantly above 9, and the normalized leaching rates after 28 days at most at a level of 2.78·10−6 g·cm−2·day−1. The composites exhibit relatively good radiation resistance against doses up to ca. 100 kGy, after which their mechanical properties (stress at 100% elongation, tensile strength and elongation at break) drop, with a significant increase of the hardness and crosslinking density. The composites exhibit good radiation shielding properties, especially in case of the heavy weight bismuth oxide filler. The proposed methodology has a strong potential to be successfully applied for radioactive waste stabilization in industrial scale.

Decay of Nonnegative Solutions of Singular Parabolic Equations with KPZ-Nonlinearities

The Cauchy problem for quasilinear parabolic equations with KPZ-nonlinearities is considered. It is proved that the behavior of the solution as $$t \to \infty $$ can change substantially as compared with the homogeneous case if the equation involves zero-order terms. More specifically, the solution decays at infinity irrespective of the behavior of the initial function and the rate and character of this decay depend on the conditions imposed on the lower order coefficients of the equation.

Prediction of recombinant Mycobacterium tuberculosis α-crystallin oligomer chaperone activity using polynomial graphs.

Background: Mycobacterial α-crystallin (Acr) is a chaperone that prevents misfolding of proteins when Mycobacterium tuberculosis is found in a latent form in the host tissue. Methods: Using insulin as a model substrate and utilizing polynomial graphs, we attempted to predict molecular-level interactions that are a function of the oligomeric state of the recombinant protein. The chaperone activity of the recombinant oligomeric Acr was measured at 60°C with Acr samples obtained before gel filtration chromatography and compared with a gel-filtered sample. Results: The polynomial graphs constructed showed improved molecular coverage of the insulin B chain by the oligomer. The 2 nd order coefficient is the one that changes with the oligomeric ratio of Acr and improves chaperone activity. Polynomial analysis suggested that it could be a useful parameter to predict chaperone activity for potential in vitro batches of M. tuberculosis Acr based on the dynamic nature of the association and disassociation of oligomers. Conclusions: The results showed that coverage of insulin B chain improved with higher ratio of 9-mer as compared to lower ratios. This was shown by both simulation plots and actual assay data. The polynomial graphs showed increase in the 2 nd order coefficient, thus suggesting the important role of oligomerisation in improved molecular coverage of insulin B chain.

Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains

We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to $L^q$ with $q \in [2,\infty)$, we prove a pointwise asymptotic estimate of the solution at the spatial infinity in terms of the behavior of the coefficients. As a corollary, we obtain the Liouville-type theorem in the case when the coefficients may grow at the spacial infinity. We also study a corresponding parabolic problem in the $n$-dimensional whole space and discuss the energy identity for solutions in $L^q$. As a corollary we show also the Liouville-type theorem for both forward and ancient solutions.

ON THE CONSTRUCTION OF A FUNDAMENTAL SYSTEM OF SOLUTIONS OF A LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS OF AN ARBITRARY ORDER

The paper proposes a method of presentation topics «On the construction of a fundamental system of solutions of a linear homogeneous differential equation with constant coefficients of an arbitrary order». In the traditional presentation of this topic in the case when the characteristic equation has complex roots, the particular solutions of the equation corresponding to them are constructed by applying the elements of complex analysis. In consequence of that, for students in the field, whose training programs included the theory of linear differential equations with constant coefficients and at the same time does not include the study of the theory of complex analysis, types of private solving the equation in this case is given without substantiation, or as a known fact, only for this case, previously issued elements complex analysis. Offered in the presentation technique differs from the traditional presentation of the topic in that it partial solutions scheme for constructing fundamental system of homogeneous linear equation with constant coefficients of arbitrary order is based only on the basis of the properties of the differential form corresponding to the left side of the equation, without using the elements of the theory of complex analysis.

Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size

Abstract In 2009, Grant, Shallit, and Stoll [Acta Arith. 140 (2009), [345–368] constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2 in cases where the size of the alphabet is a prime number or a squarefree product of primes. We establish similar results for an even larger family of pseudorandom sequences, constructed via difference matrices, in the case of an alphabet of any size. The constructions generalize those from Grant et al. In the case where the size of the alphabet is squarefree and where there are at least two prime factors, we obtain an improvement in the error term by comparison with the result of Grant et al.

Reliability Assessment of GaAs/Al₂O₃ Junctionless FinFET in the Presence of Interfacial Layer Defects and Radiations

This research work reports reliability assessment of junctionless (JL) FinFET in the presence of interfacial trap charges and radiations. The degradation in performance of JL FinFET is evaluated by calculating various figure of merit. Linearity behavior of the device is studied by considering higher order coefficient of transconductance, VIP2, VIP3, IIP3, IMD3. Also, a comparative analysis of various structures obtained by considering different semiconductor/oxide combinations is performed. Impact of interface trap charges and radiations on performance of these devices is carried out in detail. Results show that, the structure having higher value dielectric oxide provides better immunity to trap charges. The mechanism of Single event transients is also studied in JL FinFET and result show that the peak value of transient current increases with increase in LET values.

Linear quasi-randomness of subsets of abelian groups and hypergraphs

We establish an equivalence between the two seemingly distant notions of quasi-randomness: small linear bias of subsets of abelian groups and uniform edge distribution for uniform hypergraphs.For a subset A⊂G of an abelian group G consider the k-uniform Cayley (sum) hypergraph H(k)(A). The vertex set of H(k)(A) is G and the edges are k-element sets {x1,…,xk}∈Gk with x1+⋯+xk∈A. For d∈(0,1) we show that sets A⊂G of density d+o(1) have all non-trivial Fourier coefficients of order o(|G|) if and only if e(U)=d|U|k+o(|G|k) for all U⊂V(H(k)(A)).This connects the work of Chung and Graham on quasi-random subsets of the integers and that of Conlon–Hàn–Person–Schacht on weak/linear quasi-random hypergraphs. Further, it extends the work of Chung and Graham who established the corresponding result for k=2 and G=Zn.

Reduced hardware costs with software and hardware implementation of digital methods multistage discrete Fourier transform on programmable logic devices

Let us consider questions, which are connected to the research of terms of hardware and software implementation digital signal processing (DSP) methods. Theoretical basis of this research are methods of non-recursive difference of digital filtration with integer difference coefficients different orders of difference and methods of multistage discrete Fourier transform (DFT) based on such digital filtration. The purpose of the study is the research and formalization of necessary and sufficient condition of lowering hardware costs in hardware and software implementation of methods multistage DFT of digital signals on programmable logic devices (PLD). For reaching the research goal there are used methods of direct search and comparative analysis of results of such realization of methods of multi-stage DFT of digital multi-band signals, while filtering these signals, which are based on their non-recursive difference digital filtering with integer difference values coefficients and different orders of magnitude of difference. There are described abilities and specialties of PLD, which are built using architecture of a coarse-grained or fine-grained architecture or using combined architecture, which connects the convenience of implementing digital processing algorithms signals on the basis of tables of code conversion and reconfigurable memory modules. It is clear that a necessary and sufficient condition of lowering hardware costs in terms of hardware and software realization of methods for multi-stage DFT of digital signals on PLD is the triviality of meanings of integer difference coefficients of a non-recursive difference digital high difference orders’ filtration, which ensure this information. There is mentioned a formula, which allows making such condition. The practical significance of the research results consists of defining the necessary and sufficient condition of lowering hardware costs in terms of hardware and software implementation on PLD methods of multi-stage DFT signals based on their non-recursive digital difference filtering with integer values differential coefficients of various orders of magnitude difference. The novelty of research results lies in formalization of this condition. The reliability of the research results confirms their compliance with the results of well-known developments of DSP methods.