Effect of hydrostatic stress on yield function and plastic constitutive relations

A new yield function taking effect of hydrostatic stress into account is presented through establishing and solving the functional equation satisfied by the yield function, and its characteristic is simple in form and strong in generality. In order to reveal its availability, a comparison is made between the results obtained with it and the experimental results of grey cast iron has be done, both seem to be in good agreement. At the same time, taking the yield function obtained here as a potential function, a new associative plastic constitutive equation taking effect of hydrostatic stress into account is built, and the plastic volume change ratio of plastic deformation is given.

Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind

In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.

Relationship between Traffic Related Air Pollutants and Cognitive Function among Elderly in Egypt

Background: Cognitive impairment is a major health issue particularly with the increasing aging population. There are around 47.5 million dementia cases globally. Traffic air pollution issue is a chief environmental problem principally in the mega cities such as Cairo. Methodology: In a Cross sectional and comparative research study the study subjects recruited involved 200 individuals, categorized into two research groups: 100 from Cairo’s elderly home residents and 100 from EL-Gharbaya’s elderly home residents. Results: Statistical linear regression analysis revealed that fine particulate matter, carbon monoxide, and nitric oxide have a statistically significant impact on cognitive function (p values Conclusions: Traffic related air pollutants were strongly associated with cognitive impairment within elderly population in geriatric home residents in Egypt. Regarding to statistically significant difference in concentration of traffic related air pollutants between urban and rural areas, urban areas were more polluted than rural areas.

Relations and Functions

Using ordered pairs,we can formulate themathematical theory of relations in set-theoreticlanguage.By a relation we mean here something likemarriage (between men and women) or belonging(between elements and sets).Looking at any specific relation,such asmarriage for instance,we might be tempted toconsider certain ordered pairs (x,y),namely justthose for which x is a man,y is a woman,and x ismarried to y.We have not yet seen the definition

On Enforcing Dyadic-type Homogeneous Binary Function Product Constraints in MatBase

Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.

A New Citation Recommendation Strategy Based on Term Functions in Related Studies Section

Purpose:Researchers frequently encounter the following problems when writing scientific articles:(1)Selecting appropriate citations to support the research idea is challenging.(2)The literature review is not conducted extensively,which leads to working on a research problem that others have well addressed.The study focuses on citation recommendation in the related studies section by applying the term function of a citation context,potentially improving the efficiency of writing a literature review.Design/methodology/approach:We present nine term functions with three newly created and six identified from existing literature.Using these term functions as labels,we annotate 531 research papers in three topics to evaluate our proposed recommendation strategy.BM25 and Word2vec with VSM are implemented as the baseline models for the recommendation.Then the term function information is applied to enhance the performance.Findings:The experiments show that the term function-based methods outperform the baseline methods regarding the recall,precision,and F1-score measurement,demonstrating that term functions are useful in identifying valuable citations.Research limitations:The dataset is insufficient due to the complexity of annotating citation functions for paragraphs in the related studies section.More recent deep learning models should be performed to future validate the proposed approach.Practical implications:The citation recommendation strategy can be helpful for valuable citation discovery,semantic scientific retrieval,and automatic literature review generation.Originality/value:The proposed citation function-based citation recommendation can generate intuitive explanations of the results for users,improving the transparency,persuasiveness,and effectiveness of recommender systems.

RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L_2-METRIC

For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d） （1≤ q ≤ ∞）, and obtain its weak asymptotic result.

Glucomannan for abdominal pain-related functional gastrointestinal disorders in children:A randomized trial

AIM:To assess the efficacy of glucomannan(GNN) as the sole treatment for abdominal pain-related functional gastrointestinal disorders(FGIDs).METHODS:We conducted a double-blind,placebocontrolled,randomized trial.Patients were recruited among children referred to the Department of Paediatrics,Medical University of Warsaw.Included in the study were children aged 7-17 years with abdominal pain-related FGIDs classified according to the Rome Ⅲ diagnostic criteria.The children were randomly assigned to receive GNN,a polysaccharide of 1,4-D-glucose and D-mannose,a soluble fiber from the Japanese Konjac plant,at a dosage of 2.52 g/d(1 sachet of 1.26 g 2 times a day),or a comparable placebo(maltodextrin) at the same dosage.The content of each sachet was dissolved in approximately 125 mL of fluid and was consumed twice daily for 4 wk.RESULTS:Of the 89 eligible children,84(94%) completed the study."No pain" and "treatment success"(defined as no pain or a decrease ≥ 2/6 points on the FACES Pain Scale Revised) were similar in the GNN(n = 41) and placebo(n = 43) groups [no pain(12/41 vs 6/43,respectively;RR = 2.1,95%CI:0.87-5.07) as well as treatment success(23/41 vs 20/43;RR = 1.2,95%CI:0.79-1.83)].No significant differences between the groups were observed in the secondary outcomes,such as abdominal cramps,abdominal bloating/gassiness,episodes of nausea or vomiting,or a changed in stool consistency.GNN demonstrated no significant influence on the number of children requiring rescue therapy,school absenteeism,or daily activities.CONCLUSION:In our setting,GNN,as dosed in this study,was no more effective than the placebo in achieving therapeutic success in the management of FGIDs in children.

SOME IDENTITY RELATIONS BETWEEN PLANE PROBLEMS FOR VISCO-AND ELASTICITY

In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(Xu t). Secondly some identity relations betweendisplacements and stresses for plane problems of sisco-and elasticity are discussed indetait and some meaningful conclusions are obtained As an example the deformationresponse for viscoelastic plate with a small circular hote at the center is analyzed undera uniasial uniform extension.

The empirical relationships between M_S,m_band M_L for China and vicinity

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A Functional Analysis of English Relative Clauses

Relative clauses in traditional grammars,which are sometimes called attributive clauses,are divided into two types:restrictive and non-restrictive.Building upon the discussion of recursion in Halliday’s Systemic Functional Grammar(SFG),this paper conducts a functional syntactic analysis of such clauses,aimed at probing into their logical structures.

Phonon dispersion relations and soft modes of 4 carbon nanotubes

The phonon dispersion relations of three kinds of 4 A carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the （5,0） tube which are quite different from those reported previously. Our results suggest that the （5,0） tube remains metallic at very low temperature, instead of the metallie-semiconducting transition claimed before.

Rayleigh reciprocity relations： Applications

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation： higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green＇s function retrieval from volume noises.

Mathematical expression for the relationship between internode number and internode length for bamboo, Phyllostachys pubescens

We analyzed the relationship between internode number and intemode length for one of the largest bamboo, Phyllostachys pubescens Mazel ex Houz. For 50 sample culms with various sizes felled in a pure stand of P. pubescens, the intemode number was assigned from base to tip and the length for each internode was directly measured. The result indicated that the intemode length should be cumulated from base to tip, and then the cumulated internode length should be relativized by the total culm length. It was inappropriate to relativize the internode length by the maximum intenode length. In addition, the relationship between the relative internode number （the intemode number relativized by the total number of intemodes） and the relative cumulated internode length should be described not by a power function but by a sigmoid function such as the third-order function. The determined function enabled us to estimate the actual internode length, with the root mean squared error being 4 cm. In conclusion, the mathematical expression presented here, i.e., the relativization of the cumulated internode length by the total culm length and the application of the sigmoid function, will be useful in describing the relationship between internode number and internode length for P. pubescens.

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials.The phonon dispersion relation,as well as the vibrational density of states,is also often used as an indicator of variation of lattice thermal conductivity with the external stress,defects,etc.In this study,a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package.The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present.The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell.Then,the phonon dispersions corresponding to several potentials or force fields,which are commonly used in the LAMMPS package to modeling the graphene,are obtained to compare with that from the DFT calculation.They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation.The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell,which predicts the phonon band gaps along the cross-plane direction.Since the phonon dispersion relation plays an important role in the physical properties of condensed matter,the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.

Rational design of heterogeneous catalysts by breaking and rebuilding scaling relations

Various scaling relations have long been established in the field of heterogeneous catalysis,but the resultant volcano curves inherently limit the catalytic performance of catalyst candidates.On the other hand,it is still very challenging to develop universal descriptors that can be used in various types of catalysts and reaction systems.For these reasons,several strategies have recently been proposed to break and rebuild scaling relations to go beyond the top of volcanoes.In this review,some previously proposed descriptors have been briefly introduced.Then,the strategies for breaking known and establishing new and more generalized scaling relations in complex catalytic systems have been summarized.Finally,the application of machine-learning techniques in identifying universal descriptors for future computational design and high-throughput screening of heterogeneous catalysts has been discussed.

On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments

In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.

Associated Hermite Polynomials Related to Parabolic Cylinder Functions

In analogy to the role of Lommel polynomials ?in relation to Bessel functions Jv(z) the theory of Associated Hermite polynomials in the scaled form ?with parmeter v to Parabolic Cylinder functions Dv(z) is developed. The group-theoretical background with the 3-parameter group of motions M(2) in the plane for Bessel functions and of the Heisenberg-Weyl group W(2) for Parabolic Cylinder functions is discussed and compared with formulae, in particular, for the lowering and raising operators and the eigenvalue equations. Recurrence relations for the Associated Hermite polynomials and for their derivative and the differential equation for them are derived in detail. Explicit expressions for the Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given and by means of them the Parabolic Cylinder functions are represented by two such basic functions.