We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a c...

The purpose of this paper is to introduce and study regular bopen sets (briefly rb-open sets) in topological spaces and obtain some of their properties. We introduce the rb-closure and discuss some basic properties of the rb-closure. Also we study the new concepts of rb-closed spaces by means of filter bases. Mathematics Subject Classification: 54A05, 54A20

of zeros of d F ( e j W ) / d w [2]. Generally speaking, the maximally In this paper, we derive some properties of maximally flat R-regular Mth-band FIR filters. We show that the R-regularity implies maximally flat frequency response at w = 0. The R-regular constraints are a set of linear equations with complex coefficients. We can convert these complex-value equations to equivalent ones with o...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of scalar fields (“feature channels”), whereas the steerable G-CNN can also use v...

We present a design scheme to generate tight and semi-tight frames in the space of discrete-time periodic signals, which are originated from four-channel perfect reconstruction periodic filter banks. The filter banks are derived from interpolating and quasi-interpolating polynomial and discrete splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) an...

Planetary flows--atmospheric and oceanic--are approximately two-dimensional and dominated by coherent concentrations of vorticity. Data assimilation attempts to determine optimally the current state of a fluid system from a limited number of current and past observations. In this two-part paper, an advanced method of data assimilation, the extended Kalman filter, is applied to the Lagrangian re...

The development of an algorithm for automatic detection of sperm whale clicks in large recordings is described. It is based on the Teager–Kaiser (TK) energy operator and it is able to detect efficiently creaks as well as regular clicks. A matching filter is first used as a pre-processor in order to overcome the difficulties caused by the multi-pulse structure of regular clicks. Next, the TK ene...

Pressure ulcers have been identified as a public health concern by the US government through the Healthy People 2010 initiative and the National Quality Forum (NQF). Currently, no tools are available to assist clinicians in erythema, i.e. the early stage pressure ulcer detection. The results from our previous research (supported by NIH grant) indicate that erythema in different skin tones can b...