The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular,p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and onl...

A singular Cauchy-Nicoletti problem for a system of three ordinary differential equations is considered. An approach which combines topological method of T. Ważewski and Schauder’s principle is used. Theorem concerning the existence of a solution of this problem (a graph of which lies in a given domain) is proved. Moreover, an estimation of its coordinates is obtained.

A new processor for detecting a radar target in correlated, non-Gaussian noise is obtained. When this processor and a matched filter are excited with this noise, performance is improved over that of the matched filter alone. The processor is obtained by developing an approximate, bivariate, probability density for the noise and constructing a Neyman-Pearson test and then using an approximation ...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...

This paper presents a method for extracting the coupling matrix and the unloaded Q from the measured (or electromagnetic simulated) S-parameters of a narrow band cross-coupled resonator bandpass filter with losses. The Cauchy method is applied to determine the characteristic polynomials of the S-parameters of a filter in the normalized low-pass frequency domain. A five-parameter optimization me...

Many motion object detection algorithms rely on the process of background subtraction, an important technique which is used for detecting changes from a model of the background scene. The background model affects object detecting algorithm tolerating changes in background scene and the granularity of the detected foreground objects. An algorithm using a subtracted background modeling based on C...

In the paper we show equivalence of the convergence of filters on a topological space and the convergence of nets in the space. We also give, five characterizations of compactness. Namely, for any topological space T we proved that following condition are equivalent: • T is compact, • every ultrafilter on T is convergent, • every proper filter on T has cluster point, • every net in T has cluste...

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...