Solvability dependencies between dichotomous test items play an important role in the psychometric theory of knowledge spaces. Knowledge space theory (KST), based on hypothesized solvability dependencies between dichotomous items, has been successfully applied for the computerized, adaptive assessment and training of knowledge. For instance, see the ALEKS system, a fully automated math tutor on...

the aim of this paper is to show how some measures of noncompactness in the banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . the results obtained generalize and extend several equations . an illustrative example is also presented .

Let E be a locally convex space and f : E → E a mapping. We say that the equation f(x) = 0 is almost solvable on A ⊂ E if 0 ∈ f(A). In this paper some results about the solvability and almost solvability are given. Our results are based on some classical fixed point theorems and on some geometrical conditions.

An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is improved. This enhanced solvability result allows the design of a robust iterative method for the numerical solution of the algebraic inclusion. Sharp error estimates for this method, illustrative analytic examples and a numerical example are provided.

We study the solvability of the equation x′′ = f(t,x,x′) subject to Dirichlet, Neumann, periodic, and antiperiodic boundary conditions. Under the assumption that f can be suitably decomposed, we prove approximation solvability results for the above equation by applying the abstract continuation type theorem of Petryshyn on A-proper mappings.

The purpose of this article is to provide criteria for the solvability of the Diophantine equation a2X2− bY 2 = c in terms of the simple continued fraction expansion of √ a2b, and to explore criteria for the solvability of AX2 − BY 2 = C for given A, B, C ∈ N in the general case. This continues work in [9]–[11].

The row by row decoupling problem (RRDP) for descriptor systems is considered using proportional state feedback and input transformation. Necessary and sufficient conditions for the solvability of the RRDP are provided. These solvability conditions can be readily verified. A constructive solution to the RRDP is given so that the desired feedback and input transformation matrices can be obtained...

Abstract. For second order nonlinear differential equations with nonintegrable singularities with respect to the time variable, unimprovable sufficient conditions for solvability and unique solvability of multi-point boundary value problems are established. îâäæñéâ. éâëîâ îæàæï ŽîŽûîòæãæ áæòâîâêùæŽèñîæ àŽêðëèâIJâIJæïŽåãæï ŽîŽæêðâàîâIJŽáæ ïæêàñèŽîëIJâIJæå áîëæåæ ùãèŽáæï éæéŽîå áŽáàâêæèæŽ éîŽãŽèû...

The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these theorems to proving solvability and nontrivial solvability of the Dirichlet problem for ordinary and partial differential equations are considered.