Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES

In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)

In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.

Characterizations of Weighted Besov Spaces with Variable Exponents

In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavelet.As an application,we obtain the boundedness of the pseudo-differential operators on these spaces.

The Determination Method of Product Engineering Features Based on Linguistic Variables

To overcome the problem of imprecise and unclear information in the development of quality functions,a method for determining the priority of engineering features based on mixed linguistic variables is proposed.First,the evaluation member uses the determined linguistic variable to give the correlation strength evaluation matrix of customer requirements and engineering features.Secondly,the relative importance of the evaluation member and customer requirements are aggregated.Finally,the priority of engineering features is obtained by calculating the deviation.The feasibility and practicability of this method are proven by taking the design of a new product of a long bag low-pressure pulse dust collector as an example.

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.

ON THE CLASS φ_p~＊（α，β，γ，ε，η；A） of p－VALENT FUNCTIONS WITHREFERENCE TO THEBERNARDI INTEGRAL OPERATOR

Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the func-tion g(z) given byIn this paper, we extend Bernardi's theorem to certain class φp (α,β,γ,ε,η; A) of p- valent starlike functions for operators. We prove that if f(A) e φp (α, β,γ, ε, η; A), then g(A), defined byalso belongs to φp (α, β, γ, ε, η; A) and give a sufficient and necessary vondition with reference to f(A) 6 γp (α,β,γ,ε,η;A)

APPROXIMATION BY FABER-LAURENT RATIONAL FUNCTIONS IN THE MEAN OF FUNCTIONS OF CLASS LP(T) WITH 1

Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).

FRACTIONAL INTEGRALS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES

In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.

Synchronous measurements of prefrontal activity and pulse rate variability during online video game playing with functional near-infrared spectroscopy

Interactions between the central nervous system(CNS)and autonomic nervous system(ANS)play a crucial role in modulating perception,cognition,and emotion production.Previous studies on CNS–ANS interactions,or heart–brain coupling,have often used heart rate variability(HRV)metrics derived from electrocardiography(ECG)recordings as empirical measurements of sympathetic and parasympathetic activities.Functional near-infrared spectroscopy(fNIRS)is a functional brain imaging modality that is increasingly used in brain and cognition studies.The fNIRS signals contain frequency bands representing both neural activity oscillations and heartbeat rhythms.Therefore,fNIRS data acquired in neuroimaging studies can potentially provide a single-modality approach to measure task-induced responses in the brain and ANS synchronously,allowing analysis of CNS–ANS interactions.In this proof-of-concept study,fNIRS was used to record hemodynamic changes from the foreheads of 20 university students as they each played a round of multiplayer online battle arena(MOBA)game.From the fNIRS recordings,neural and heartbeat frequency bands were extracted to assess prefrontal activities and shortterm pulse rate variability(PRV),an approximation for short-term HRV,respectively.Under the experimental conditions used,fNIRS-derived PRV metrics showed good correlations with ECG-derived HRV golden standards,in terms of absolute measurements and video game playing(VGP)-related changes.It was also observed that,similar to previous studies on physical activity and exercise,the PRV metrics closely related to parasympathetic activities recovered slower than the PRV indicators of sympathetic activities after VGP.It is concluded that it is feasible to use fNIRS to monitor concurrent brain and ANS activations during online VGP,facilitating the understanding of VGP-related heart–brain coupling.

On the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

Correlation between the Six-Minute Walk Test and Subjective Functional Class in Patients with Heart Failure

Introduction: The Six-Minute Walk Test (6MWT) is an inexpensive method to objectively evaluate physical capacity or limitation and stratify prognosis in patients with Heart Failure (HF). Since the clinical perception of symptoms may be adapted or compromised, regular evaluation from medical interviews often fails to determine functional classification. This study aimed to assess the correlation between New York Heart Association Functional Class (NYHA-FC) and the distance walked in the 6MWT. Methods: We conducted a cross-sectional observational study that included patients with HF with reduced ejection fraction followed up at an outpatient service of a teaching hospital, from August 2018 to April 2019. Patients in NYHA-FC I, II, or III were included. We compared NYHA-FC subjectively obtained during the consultation with the 6MWT performed after medical consultation, and the correlation between these two parameters was assessed. Results: The study included 70 patients with HF, 41 (58.6%) of whom were female. The mean age was 61.2 ± 12.7 years. The most prevalent etiologies were dilated idiopathic cardiomyopathy (35.7%) followed by ischemic cardiomyopathy (25.7%). The mean ejection fraction was 34.1% ± 9.8%. The average distance walked in the 6MWT by NYHA-FC I patients was 437.8 ± 95.8 meters, NYHA-FC II 360.1 ± 96.4, and NYHA-FC III 248.4 ± 98.3. Functional class measured by the 6MWT was different than that estimated by NYHA-FC in 34 patients (48.6%), 23 (32.9%) for a higher functional class and 11 (15.7%) for a lower one (p = 0.07). Pearson’s correlation coefficient between NYHA-FC and the 6MWT was -0.55. Conclusion: There was a moderate correlation between the subjective NYHA-FC and the 6MWT. The 6MWT revealed a different classification from NYHA-FC in almost half of the patients. Among those who presented discrepancies between methods, 6MWT reclassification towards a higher functional class was more common.

Comparison of skeletal, dental and soft tissue changes in young adults with Class II malocclusion, treated either by camouflage, fixed functional appliance or orthognathic surgery—A prospective study on Indian subjects

Introduction: Borderline Class II malocclusion due to deficient mandible can be treated either by orthodontic camouflage, fixed functional appliances or by orthodontics followed by surgical mandibular advancement. Methodology: A prospective study was designed on young adults with Class II malocclusion on account of a deficient mandible. A total of 45 subjects were divided into three groups of 15 individuals each. The patients were treated either by camouflage, fixed functional appliances or by orthognathic surgery. Pre and post treatment cephalograms were used to assess the skeletal, dental and soft tissue changes. Pre and post treatment profile photographs were assessed on a Visual Analogue Scale (VAS) by orthodontists, oral surgeons and laypersons. Results: Each group achieved a reduction in facial convexity, but the results obtained from the surgical group were more pronounced than the camouflage and the fixed functional group. Conclusion: The reduction in convexity in the camouflage group was by retracting the upper anteriors, which increases the nasolabial angle. In the fixed functional appliance a combination of skeletal and dentoalveolar changes can be observed. However the most appropriate reduction in profile convexity can be obtained by combined orthodontic and surgical treatment of malocclusion.

A New Approach for Solving Fuzzy Linear Multi-Criterion Problems: An Approach Based on Minimization of the Errors Functions

The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.

HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES

In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.

CONVERGENCE OF A CLASS OF MEANS OF H^p FUNCTIONS(0

In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.

Diatoms as indicators of environmental change in coastal areas:a case study in Lianjiang coast of East China Sea

Owing to the significant differences in environmental characteristics and explanatory factors among estuarine and coastal regions,research on diatom transfer functions and database establishment remains incomplete.This study analysed diatoms in surface sediment samples and a sediment core from the Lianjiang coast of the East China Sea,together with environmental variables.Principal component analysis of the environmental variables showed that sea surface salinity(SSS)and sea surface temperature were the most important factors controlling hydrological conditions in the Lianjiang coastal area,whereas canonical correspondence analysis indicated that SSS and pH were the main environmental factors affecting diatom distribution.Based on the modern diatom species–environmental variable database,we developed a diatom-based SSS transfer function to quantitatively reconstruct the variability in SSS between 1984 and 2021 for sediment core HK3 from the Lianjiang coastal area.The agreement between the reconstructed SSS and instrument SSS data from 1984 to 2021 suggests that diatombased SSS reconstruction is reliable for studying past SSS variability in the Lianjiang coastal area.Three low SSS events in AD 2019,2013,and 1999,together with an increased relative concentration of freshwater diatom species and coarser sediment grain sizes,corresponded to two super-typhoon events and a catastrophic flooding event in Lianjiang County.Thus,a diatom-based SSS transfer function for reconstructing past SSS variability in the estuarine and coastal areas of the East China Sea can be further used to reflect the paleoenvironmental events in this region.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.