SOME BOUNDED RESULTS OF θ(t)-TYPE SINGULAR INTEGRAL OPERATORS

1　ＴｈｅＣｏｎｃｅｐｔｉｏｎｓａｎｄＲｅｓｕｌｔｓＬｅｔＢｂｅａＢａｎａｃｈｓｐａｃｅｉｎＵＭＤ(ｕｎｃｏｎｄｉｔｉｏｎａｌｉｔｙｏｆｍａｒｔｉｎｇａｌｅｄｉｆｆｅｒｅｎｃｅｓ)ｗｉｔｈａｎｕｎｃｏｎｄｉｔｉｏｎａｌｂａｓｉｓ.Ｂ＿ｖａｌｕｅｄｆｕｎｃｔｉｏｎｆ(ｘ)ｏｎＲｎｉｓｓａｉｄｔｏｂｅｉｎＬｐＢ(Ｒｎ),(1≤ｐ< ∞)ｉｆ‖ｆ‖ＬｐＢ=∫Ｒｎ‖ｆ(ｘ)‖ｐｄｘ1/ｐ< ∞　(1≤ｐ< ∞),ａｎｄｔｈｅｎｏｒｍａｓ　‖ｆ‖ＬｐＢ=∫Ｒｎ‖ｆ(ｘ)‖ｐｄｘ1/ｐ　(1≤ｐ< ∞).　　Ｆｏｒｔｈｅｓｉｎｇｕｌａｒｉｎｔｅ…     

Some qualitative results for a modification of the Green–Lindsay thermoelasticity

In this short note we consider a recent modification of the Green–Lindsay thermoelastic theory proposed at Yu et al. (Meccanica 53:2543–2554, 2018). We consider a functional defined on the solutions of the problem. It allows us to obtain the continuous dependence of the solutions with respect to the initial conditions and to the supply terms, the time exponential decay of solutions and an alternative of Phragmén–Lindelöf type for the spatial behaviour.     

Comprehensive mathematical model of microcirculatory dynamics (II)—Calculation and the results

The mathematical model described in Part I was solved using “influence line method” combining analytical method and finite element method. Many important aspects of microcirculatory dynamics were analyzed and discussed. It show that interstitial fluid pressure changes its sign twice within one arteriolar vasomotion period and it is therefore not important that interstitial fluid pressure is a little higher or lower than atmospheric pressure; arteriolar vasomotion can periodically result in lymph formation and interstitial total pressure plays an important role in this procedure; local regulation of microcirculation can meet metabolic need some extent in the form of dynamic equilibrium. The property of arteriole as a “resistant vessel” and the efficiency of microvascular network as heat exchanger are also shown. These results show that the comprehensive mathematical model developed in Part I is physiologically resonable. Foundation item: the Natural Science Foundation of Sichuan Province, P R China Biography: Guo Zhongsan (1947-)     

Bézier curves in the modification of boundary integral equations (BIE) for potential boundary-values problems

The paper presents a modification of the classical boundary integral equation method (BIEM) for two-dimensional potential boundary values problems. The proposed modification consists in describing the boundary geometry by means of Bézier curves. As a result of this analytical modification of the BIEM, a new parametric integral equation system (PIES) was obtained. The kernels of these equations include the geometry of the boundary. This new PIES is no longer defined on the boundary, as in the case of the BIEM, but on the straight line for any given domain. The solution of the new PIES does not require a boundary discretization since it can be reduced merely to an approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with exact solutions.     

Numerical methods for solving singular integral equations obtained by fracture mechanical analysis of cracked wedge简

The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are: (i) a radial crack on a wedge with a non-finite radius under the traction-traction boundary condition, (ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and (iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response.     

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part II: Applications and results

The paper presents an enhanced beam-theory (EBT) model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. Analytical expressions for the compliance, energy release rate, and mode mixity are deduced. A compliance calibration strategy enabling numerical or experimental evaluation of the interface elastic constants is also presented. Furthermore, analytical expressions for the crack length correction parameters—analogous to those given by the corrected beam-theory (CBT) model for unidirectional laminated specimens—are furnished for multidirectional laminated specimens, as well. Lastly, an example application to experimental data reduction is presented.     

ON THE SOLUTION OF NONLINEARTWOPOINT BOUNDARY VALUE PROBLEM──u" g(t.u) = f(t),u(0) = u(2π) = 0

I.IntroductionLetHbearealHilbertspace,XandYtwoclosedsubspacesofHsuchthatH=X$Y,T:H-HaC'mapping,n>1.Assumethatthereexisttwopositiveconstantsniland)liZsuchthatforVueH,Vx6X,VYey'Undertheconditions(l.1),(l.2)and(l.3),ManasevichprovedthatTisaC"diffeomorphismontoH'tl].ThepurposeofthispaperistoimprovetheaboveManasevich'shomeomQrphismtheorem,andthen,itisusedtoproveanexistenceanduniquenessresultforthenonlineartulopointboundaryvalueproblem11.ANonVariationalVersionofaMax-MinPrincipleToimprov…     

Stability of Navier-Stokes Equation(Ⅱ)

ＳＴＡＢＩＬＩＴＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮ（ＩＩ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）;ＦａｎｇＸｉａｏ－ｚｕｏ（方晓佐）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ）,Ｓｈａｎｇｈａｉ（ＲｅｃｅｉｖｅｄＤｅｃ．１１,１９９３;Ｃｏｍｍｕｎ...     

Stability of Navier-Stokes Equation(Ⅰ)

ＳＴＡＢＩＬＩＴＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮ（Ⅰ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＤｅｃ．１０，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉ－ｚａ...     

Phragmén-Lindel(o)f and continuous dependence type results in a Stokes flow

This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder.With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder,solutions either grow or decay exponentially in the distance from the finite end of the cylinder.In the case of decay,the effect of perturbing the equation parameters is also investigated.     

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W~(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.     

The “Arch of equilibration” of Charles Hutton (1772)

This paper is a historical re-visitation of the work of C. Hutton, a mathematician of the XVIII century, who wrote an innovative essay on the shape of arches, whose intrados he identifies with the curve of pressure, that he names “arch of equilibration”. His solution was mostly ignored by his contemporaries and after the middle of the XIX century forgotten. But Hutton’s problem is important, also because it offers the first example of an inverse problem in structural mechanics.     

Remembrances of Jens Lothe (1931–2016)

Jens Lothe, Professor Emeritus of Physics at the University of Oslo, passed away at age 84 on September 26, 2016 after a brief illness. This article presents a survey of his life, work, and influence from the standpoints of four authors who had the great fortune to be associated with him both professionally and personally. A list of his publications is included.     

The saga of internal variables of state in continuum thermo-mechanics (1893–2013)

The thermomechanics of continua with internal variables of state is often presented as an alternative to rational continuum mechanics or an extension of the classical linear theory of irreversible processes. It has become ubiquitous in the theories of dissipative mechanical phenomena such as viscoelasticity, plasticity, damage, phase transformations in deformable solids, and the rheology of many fluids. The present contribution highlights the historical development of this fruitful approach since the early works of Duhem, Bridgman, and Eckart, and then the quite definite framework more recently delineated in studies by Kestin and Muschik. It peruses the vast field of successful applications in both solid and fluid mechanics as well as in the theory of coupled fields in the second half of the twentieth century. It also necessarily envisages further generalizations of – deviations from, and contradictions with – this well defined framework with the introduction of gradients, and the difficulties posed by these in the interpretation of the variables. Globally, this pragmatic approach has proved its efficiency in dealing with complex behaviours of continua over a period that started more than a hundred years ago with ideas put forward by Duhem.

“So hidden in this hocus-pocusThere lies the gift of double focus”(W.H. Auden, New Year Letter)