One-sided Conditions Research Articles

Dynasties Intertwined: The Zirids of Ifriqiya and the Normans of Sicily

Dynasties Intertwined: The Zirids of Ifriqiya and the Normans of Sicily

Condition numbers related to the core inverse of a complex matrix

Under one-sided conditions, we establish explicit expressions for the condition numbers of the core inverse and the core inverse solution of a linear system, using Hartwig and Spindelb?ck?s decomposition, the spectral norm and the Frobenius norm. We also present the structured perturbation of the core inverse.

Accelerating business-to-business contract negotiations: Moving from one-sided to balanced standard contract terms

Many businesses adopt one-sided boilerplate contract terms and conditions that lead to protracted negotiations. Often, the parties ultimately reach a compromise that could have been reached sooner if they had put forward more balanced contract terms at the outset. We ask why this seemingly irrational behavior persists and suggest a different approach. A dominant theory suggests that putting forward balanced terms may be seen as a sign of a weak bargaining position. We argue, however, that agency conflicts and cognitive biases often better explain such behavior. Moreover, we advocate a speed-to-contract strategy where the parties elect to use more balanced (value-maximizing) terms from the outset, and thereby avoid costly negotiations as well as delays in realizing the benefits of a transaction.

Тепловая модель сквозного металлизированного отверстия печатной платы при од-ностороннем нагреве

Thermal methods of quality control of the plated-through hole (PTH) of printed circuit board (PCB) are based on thermal models. However, known thermal models of PTH take no account of heat transfer to PCB material thus not allowing for PTH heat characteristic tying up with adhesion quality. In this work, an axisymmetric thermal model of a single-layer PCB PTH under one-sided heating conditions is considered. It was shown that the ratio of the temperature increments of the upper (heated) and lower end of the PTH in the considered range of heating power does not depend on the power level. A linear thermal equivalent scheme of the PTH has been proposed, which includes the longitudinal thermal resistance of the PTH metallization, de-termined by the parameters and quality of the metallization layer, the thermal resistance, which determines the convection heat exchange between the ends of the PTH with the adjacent PCB surface and the environment, and the thermal resistance of the area of the PCB material adjacent to the PTH, depending on the quality of the metallization adhesion and the PCB dielectric. Thermal equivalent circuit parameters determined by the ratio of the temperature increment of the upper and lower ends of the PTH and their difference can serve as the basis for the development of a nondestructive inspection procedure for PTH quality control by way of its unilateral heating, for example, by a laser beam.

Local Heat Transfer Characteristic Coincidence in Helically Coiled Tubes Under Different Heating Conditions

The heat transfer and flow characteristics within a helically coiled tube are further investigated numerically in this work, under both uniform heating, and one-sided heating conditions. This work focuses on the local heat transfer characteristic coincidence that occurs at the innermost point of any fully developed cross-section, whereby the local Nusselt number remains constant regardless of the type of heating condition. This feature can be used to approximate the unknown heating flux for one heating condition with the known value for the other heating condition. Different parameters including flow states (Reynolds number), geometrical parameters of the helically coiled tube (curvature ratio, helical pitch), heating conditions (heat flux) and working fluid property (Prandtl number) that have significant impact on the heat transfer characteristics have been tested. The results show that the heat transfer characteristic coincidence does not change along with the variable parameters which indicates that the proposed correlation of local Nusselt numbers can be extended to a wide range of parameters.

Weighted inequalities for singular integral operators on the half-line

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operators satisfy relaxed Dini conditions. We apply the weighted estimates to extrapolation of maximal L p regularity of first order, second order and fractional order Cauchy problems into weighted rearrangement invariant Banach function spaces. In particular, we provide extensions, as well as a unification of recent results due to Auscher and Axelsson, and Chill and Fiorenza.

Filippov-Pliss lemma for dynamical inclusions on a time scale

In this paper we prove two variants of the well-known Filippov-Pliss lemma in the case of dynamical inclusions on a time scale. The first variant is when the right-hand side is Lipschitz continuous on the state variable. Afterward we introduce one-sided Perron conditions for multifunctions on a time scale and prove the second variant of that lemma. Some discussions on relaxed systems are presented.

New Energy Inequalities for Tensorial Wave Equations on Spacetimes that Satisfy a One-Sided Bound

We consider several tensorial wave equations, specifically the equations of Maxwell, Yang–Mills, and Weyl fields, posed on a curved spacetime, and we establish new energy inequalities under certain one-sided geometric conditions. Our conditions restrict the lapse function and deformation tensor of the spacetime foliation, and turn out to be a one-sided and integral generalization of conditions recently proposed by Klainerman and Rodnianski as providing a continuation criterion for Einstein's field equations of general relativity. As we observe it here for the first time, one-sided conditions are sufficient to derive energy inequalities for certain tensorial equations, provided one takes advantage of some algebraic properties enjoyed by the natural energy functionals associated with the equations under consideration. Our method especially applies to the Bel–Robinson energy for Weyl fields, and our inequalities control the growth of the energy in a uniform way, with implied constants depending on the one-sided geometric bounds, only.

Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and ``hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one-sided conditions that they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Toward these goals we introduce, for the first time, a fully nonsmooth, discrete Hamilton's principle and obtain an associated framework for composing geometric numerical integration methods for inequality-equality--constrained systems. Applying this framework, we formulate a new family of geometric numerical integra...

Some one-sided conditions under which subsequential convergence follows from [formula omitted] summability method

In this paper, we introduce some conditions to recover subsequential convergence of an (A,k) summable sequence which is one-sidedly bounded by another sequence.

Study of pressure drop and heat transfer in a swirl flow with one-sided heating in a range of heat flowrates below boiling crisis

A representative mass of experimental data on pressure drop and heat transfer under forced convection and boiling in a swirl water flow under one-sided heating conditions is obtained. Recommendations are given for calculating pressure drop in a swirl flow. A method of calculating heat transfer in channels with onesided heating is proposed.

Consideration of the procedural error for measuring contact sensor temperature during thermophysical studies

The procedural error is described for measuring the temperature of a contact sensor with placement within the grooves of an experimental specimen made of ceramic material. Mathematical modelling is performed for the error under specimen one-sided heating conditions. The effect is demonstrated for the error on the result of processing experimental data by means of mathematical processing of nonstationary nonlinear reverse thermal conductivity problems. Recommendations are given for reducing this error.

Existence and location results for hinged beam equations with unbounded nonlinearities

This work presents some existence, non-existence and location results for the problem composed by the fourth-order fully nonlinear equation u ( 4 ) ( x ) + f ( x , u ( x ) , u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) ) = s p ( x ) for x ∈ [ 0 , 1 ] , where f : [ 0 , 1 ] × R 4 → R and p : [ 0 , 1 ] → R + are continuous functions and s is a real parameter, with the Lidstone boundary conditions u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 . This problem models several phenomena, such as, the bending of an elastic beam simply supported at the endpoints. The arguments used apply a lower and upper solutions technique, a priori estimations and topological degree theory. In this paper we replace the usual bilateral Nagumo condition by some one-sided conditions, which enables us to consider unbounded nonlinearities.

Singular quasilinear heat equations

. With Q ⊂ R N a bounded open connected set, the initial value problem for the nonhomogeneous nonlinear heat equation ∂u/∂t - ΔM = f(x, t, u) with zero boundary conditions and zero initial condition is solved in a generalized sense in the region Ω × (0, T) under new one-sided conditions on f(x, t, s). In particular, this result greatly improves on the well-known one-sided result of Brezis and Nirenberg, [2, p. 302]. The techniques used here are completely different from those employed by the last mentioned authors and carry over even to the case when the space operator may be singular elliptic and quasilinear in the lower order terms. So the main result is presented in this singular quasilinear context.

Quasilinear elliptic inclusions of Clarke's gradient type under local growth conditions

We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient that satisfies only a one-sided local growth condition. An appropriate modification of the associated potential function along with truncation techniques will allow us to apply the theory of multivalued pseudomonotone operators for obtaining existence and comparison results under only one-sided local growth conditions on Clarke's generalized gradient.

Existence of solutions of parabolic variational inequalities with one-sided restrictions

We prove sufficient conditions for the existence of a solution of a “strong” nonlinear variational inequality of parabolic type. The theory can be used for solving parabolic equations with one-sided boundary conditions. As an example, we prove the existence of a solution of a “strong” parabolic variational inequality with p-Laplacian in the Sobolev space L p (0, T, W p 1 (Ω)), p ∈ [2, ∞).

One-sided convergence conditions of Lagrange interpolation based on Jacobi-type weights

The authors state a one-sided convergence theorem for Lagrange interpolation based on certain generalizations of Jacobi weights. In a sense the results are best possible.

One-sided strong laws forincrements of sumsof i.i.d. random variables

We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdős-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgő-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index αЄ(1,2).

One-sided Tauberian conditions and double sequences

We give a theorem of Vijayaraghavan type for summability methods for double sequences, which allows a conclusion from boundedness in a mean and a one-sided Tauberian condition to the boundedness of the sequence itself. We apply the result to certain power series methods for double sequences improving a recent Tauberian result by S. Baron and the author [4].

Critical Heat Flux in Subcooled Water Flow in a Saw-Toothed Finned Duct Under One-Sided Heating Conditions

Critical heat flux (CHF) tests on a new type of rectangular cooling tube, “a saw-toothed fin duct (SFD)” for high heat flux components, were performed under one-sided heating conditions. This tube has internal triangular fins at the heating side to enhance the CHF characteristics. The saw-toothed fin duct, which has a fin height of 3.46 mm and an installation angle of the fin of 70 deg, results in the highest CHF of 43 MW/m2 at the axial flow velocity of 10 m/sec. It was found that this value is 1.3 times higher than that of a rectangular fined tube, so-called hypervapotron. Finite element analyses on the saw-toothed fin duct were also performed to examine its thermomechanical behavior under high heat flux conditions. The results show the maximum strain amplitude in the fin bases are ranged less than 0.05% under the heat flux of 20MW/m2. From this result, the fatigue lifetime of the fin bases is estimated to be more than 106 cycles.