Mathematics

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We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in g(M, Δ ( m ), v, p). We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces. © 2018, The Author(s).

(SoNS) School of Natural Sciences

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Journal of Inequalities and Applications

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces

Wildlife corridors are components of landscapes, which facilitate the movement of organisms and processes between intact habitat areas, and thus provide connectivity between the habitats within the landscapes. Corridors are thus regions within a given landscape that connect fragmented habitat patches within the landscape. The major concern of designing corridors as a conservation strategy is primarily to counter, and to the extent possible, mitigate the effects of habitat fragmentation and loss on the biodiversity of the landscape, as well as support continuance of land use for essential local and global economic activities in the region of reference. In this paper, we use game theory, graph theory, membership functions and chain code algorithm to model and design a set of wildlife corridors with tiger (Panthera tigris tigris) as the focal species. We identify the parameters which would affect the tiger population in a landscape complex and using the presence of these identified parameters construct a graph using the habitat patches supporting tiger presence in the landscape complex as vertices and the possible paths between them as edges. The passage of tigers through the possible paths has been designed using an Assurance game, with tigers as an individual player. The game is recursively played as the tiger passes through each grid considered for the model. The iteration causes the tiger to choose the most suitable path signifying the emergence of adaptability. As a nominal explanation of the game, we design this model through the interaction of tiger with the parameters as deterministic finite automata, for which the transition function is obtained by the game payoff. © Springer Nature Singapore Pte Ltd. 2018.

Communications in Computer and Information Science

A computational approach for designing tiger corridors in India

In the present paper we characterize the compact, invertible, Fredholm and closed range weighted composition operators on Cesàro function spaces. We also make an effort to compute the essential norm of weighted composition operators. © 2018 Walter de Gruyter GmbH, Berlin/Boston.

Analysis (Germany)

Essential norm of weighted composition operators

We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, L3, using the identification of L3 with C × R. Further we give a different proof for the singular Björling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity. © 2018 International Society for Photogrammetry and Remote Sensing. All Rights Reserved.

Journal of the Ramanujan Mathematical Society

Existence of maximal surface containing given curve and special singularity

In this paper, we introduce the notion of generalized positive subdefinite matrices of level k by generalizing the definition of generalized positive subdefinite matrices introduced by Crouzeix and Komlósi in [Applied optimization. Vol. 59, Dordrecht: Kluwer Academic Publications; 2001. p. 45–63]. The main motivation behind this generalization is to identify new subclasses of row sufficient matrices [Cottle, Pang and Venkateswaran, Linear Algebra Appl. 1989;114/115:231–249] which are not a subclass of copositive matrices. We establish new sufficient conditions for a matrix to be a non-copositive P0 matrix and a non-copositive row sufficient matrix using the notion of generalized positive subdefinite matrices of level k. We present a new termination result for Lemke’s algorithm which supplements Jones’ result [Math Program. 1986;35:239–242]. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Linear and Multilinear Algebra

On generalizations of positive subdefinite matrices and the linear complementarity problem

Purpose: To determine the prevalence and incidence of epilepsy in an onchocerciasis endemic region of South Sudan. Methods: In May 2018, a door-to-door household survey was conducted in 8 study sites in an onchocerciasis endemic area in Maridi County. Results: A total of 2511 households agreed to participate in the study, corresponding to 17,652 individuals. An epilepsy screening questionnaire identified 799 persons suspected to have epilepsy (4.5\%); in 736 of the 766 persons (96.1\%) seen by a clinical officer the diagnosis of epilepsy was confirmed. Adding 38 persons who were not seen but with a positive answer to a combination of screening questions, 774 persons (4.4\%) had epilepsy. Epilepsy prevalence was highest in the 11–20 age group (10.5\%); 66 persons with epilepsy (PWE) developed their first seizures in the year preceding the survey (annual incidence = 373.9/100.000). Neurocysticercosis cannot explain the high epilepsy prevalence since no pigs are kept in the area. Independent risk factors for epilepsy included male gender, belonging to a “permanent household” and a farming family, and living in a village bordering the Maridi River. Only 7209 (40.8\%) of the population took ivermectin in 2017. Conclusion: A very high prevalence and incidence of epilepsy was observed in several villages in Maridi County located close to the Maridi River and the Maridi dam. Urgent action is needed to prevent children in Maridi County from developing OAE by strengthening the onchocerciasis elimination program. © 2018 The Authors

Seizure

High prevalence of onchocerciasis-associated epilepsy in villages in Maridi County, Republic of South Sudan: A community-based survey

This paper proposes a method for gesture classification based on Graph Fourier transform (GFT) coefficients. GFT coefficients are the projection of image pixel block onto the eigenvectors of a Laplacian matrix. This Laplacian matrix is generated from undirected graph, representing a spatial connectedness between each pixel within an image block. This work proposes a method for generating an undirected graph by using edge information of the image. Edge information of the image is obtained by average sum of absolute difference between the current pixel and its neighboring pixels by using an appropriate threshold. The resulting GFT based feature vector is formed by concatenating GFT coefficients of each block. The resultant feature vector is applied to linear Support Vector Machine (SVM) classifier to predict the gesture class. For NTU and Massey hand gesture datasets, threshold value 30 gives maximum prediction accuracy. We compare the results of the proposed GFT based descriptor approach with Karhunen-Loeve transform (K-LT) and Discrete Cosine transform (DCT) based descriptors on three different gesture datasets: NTU, Cambridge and Massey. Simulation results show that the proposed GFT based descriptor gives a comparable results with Karhunen-Loeve transform (K-LT) and Discrete Cosine transform (DCT) based descriptors for gesture classification. © 2017 IEEE.

Electrical Engineering

(SoE) School of Engineering

2017 4th International Conference on Image Information Processing, ICIIP 2017

Graph fourier transform based descriptor for gesture classification

In this paper we study seminormed double sequence spaces of a four-dimensional matrix and Musielak–Orlicz function over n-normed spaces. We explore some interesting inclusion relations, algebraic and topological properties of these spaces. © 2018, The Author(s).

Seminormed double sequence spaces of four-dimensional matrix and Musielak–Orlicz function

This paper deals with the problem of finding an integer solution to a linear complementarity problem (LCP). Chandrasekaran et al. [1] introduced the class I of integral matrices for which the corresponding LCP has an integer solution for every integral vector q, for which it has a solution and proved that for some well-known matrix classes principal unimodularity forms a necessary and sufficient condition for inclusion in the class I. In this paper, we identify some more well-known matrix classes for which principal unimodularity forms a necessary and sufficient condition for inclusion in the class I. The concept of total dual integrality is utilized to obtain a necessary and sufficient condition for existence of an integer solution to LCP with a hidden K-matrix. We interconnect the concept of Hilbert basis with principal unimodularity of a matrix and the corresponding complementary cones. A necessary and sufficient condition is given for the existence of an integer solution of a linear fractional programming problem by using its LCP formulation. © 2018 Elsevier Inc.

Linear Algebra and Its Applications

Total dual integrality and integral solutions of the linear complementarity problem

In recent years, a new theory of the evolution of microbes under normal and stressed conditions has emerged, mainly in reference with the development of fractals and of self-organized mapping (SOM) concepts. This theory has much improved our understanding of the growth pattern of microbes like bacteria which determine their dynamics of evolution. In the first part of this paper, the main ideas in the theory of microbial self-organization are outlined, and some remarkable features of the resulting growth patterns are presented. In the second part, we apply conceptual tools developed in the context of fractal geometry to the study of the scaling properties of the bacterial growth in context with SOM patterns. We observe that such growth patterns appear to be more complex than simple fractals, although in some cases a simple fractal framework may be adequate for their description. © 2018, Springer Nature Singapore Pte Ltd.