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Requiring that students enrolled in college algebra to spend hours in a computer lab has been a practice in colleges and universities to improve success and retention. In part, because students come with different backgrounds, skills, and the computer lab environment allows for personalized supplemental instruction and tutoring. However, the way this practice may cause problems among students. Prior to this study, we realized that college algebra students are not pleased with having to wait outside the lab to get in and have to spend three hours per week to a receive a small credit. The wait time is due to the limited lab capacity that cannot house a large number of students when they visit at the last minute or right after a large class meeting. Hence, we attempted to stimulate a proactive behavior of visiting the lab early in the week through offering an incentive. It entails reducing the number of lab hours for the same credit after achieving a certain mastery. The results show that the students responded well to the modification. The final exam mean test shows that the modification was an improvement.

This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples. [ABSTRACT FROM AUTHOR]

Impressed with the very recent developments of noncoercive complementarity problems and the use of recession sets in complementarity problems, here, we discuss mixed generalized complementarity problems in Hausdorff topological vector spaces. We used the Tikhonov regularization procedure, as well as arguments from the recession analysis, to establish the existence of solutions for mixed generalized complementarity problems without coercivity assumptions in Banach spaces. [ABSTRACT FROM AUTHOR]

Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the "open" balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity. [ABSTRACT FROM AUTHOR]

In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.

In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves. [ABSTRACT FROM AUTHOR]

In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter‐dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson‐type formula based on the continuity of scattering function is given. [ABSTRACT FROM AUTHOR]

This paper deals with the weak versions of the vector variational-like inequalities, namely Stampacchia and Minty type under invexity in the framework of convexificators. The connection between both the problems along with the link to vector optimization problem are analyzed. An application to nonconvex mathematical programming has also been presented. Further, the bi-level version of these problems is formulated and a procedure to obtain the solution involving the auxiliary principle technique is described in detail. We have shown that the iterative algorithm with the help of which we get the approximate solution converges strongly to the exact solution of the problem. [ABSTRACT FROM AUTHOR]

Inspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the properties of the operators satisfying this type of condition; in particular, we study the case where the space is normed, and the maps are linear. Then we generalize some theorems proposed by this author on the existence of a fixed point of one operator or a common fixed point for two operators. Our results first prove the existence of a common fixed point of a set of self-maps of any cardinal number (countable or uncountable) satisfying the conditions of Kannan type in metric spaces. The same is proved for a set of maps satisfying the mutual relations of classical contractivity. We prove in both cases the convergence of iterative schemes involving operators with mutual relations of contractivity, proposing sufficient conditions for the iteration of the operators on any element of the space to converge to the common fixed point when a different operator is taken in each step. The results obtained are applied to operators acting on real functions, coming from the fractal convolution with the null function. [ABSTRACT FROM AUTHOR]

A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented. OCIS codes: 120.2440, 100.0100, 100.5010, 100.6740.

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of tensors over a commutative ring and a noncommutative ring. Several numerical examples are provided in support of the theoretical results. We also propose algorithms for computing the inner inverses, the Moore–Penrose inverse, and weighted Moore–Penrose inverse of tensors over a noncommutative ring. The prowess of some of the results is demonstrated by applying these ideas to solve an image deblurring problem. [ABSTRACT FROM AUTHOR]

In this paper, we have proved a general theorem dealing with the ... summability factors of infinite series by using a wider class of power increasing sequences. Some new results are also obtained and some previous results are recovered. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of 2×2$2 \times 2$ block matrix A$\mathcal {A}$ in order to have the Hyers–Ulam stability. [ABSTRACT FROM AUTHOR]

In this paper, we define fractal bases and fractal frames of L²(I x J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L²(I x J) with the tensor product space L²(I) ⊗ L²(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L²(I x J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable. [ABSTRACT FROM AUTHOR]

The session initiation protocol is used for communication purposes in a client-server environment, where for each time session the client and server agree upon a shared secret session key through an authentication system. After establishing the connection between client and server for a session, both the parties use a session key to encrypt/decrypt messages for communicating within that session securely. Therefore, authentication plays a vital role in sharing the secret session key. Recently, Chaudhry et al. proposed an authentication scheme; yet this paper shows that Chaudhry et al.'s scheme has inefficient login and password change phases, respectively, and does not take care of the users' anonymity. Therefore, this study proposes an enhanced scheme, referred to as the secure authentication scheme for session initiation protocol (SAS-SIP) to eliminate the drawbacks of the scheme proposed by Chaudhry et al. In addition, the proposed SAS-SIP uses fuzzy extractors to incorporate biometric data along with the password to enhance the degree of security in the authentication system. After performing the security analysis through a random oracle model, this paper concludes that SAS-SIP is secure from secret information retrieval of communicators to the attacker. Furthermore, it has a better trade-off among several measurement costs along with security. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of mixed equilibrium problems under the extended generalized a-h monotonicity in finitely continuous topological spaces. Existence of solutions to the problems is established by relaxing the convexity structure and the linearity condition by using the relatively Knaster-Kuratowski-Mazurkiewicz principle. We also propose an iterative scheme based on auxiliary principle techniques. The results obtained in this paper improve and generalize some recent results in the framework of FC spaces under weaker conditions. They are useful to solve problems, where the domain and range of the underlying mappings lack the convexity structure. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce a new general integral operator for multivalent functions. The new suffcient conditions for the operator Jp, γ, gαi, βi (ƒ1, ƒ2, ..., ƒn) when γ = 1 is determined for the class of p-valently star-like, p-valently close-to-convex, uniformly p-valent close-to-convex and strongly starlike of order δ (0 < δ ≤ 1) in U. Our results generalize the results of Frasin [7]. [ABSTRACT FROM AUTHOR]

In the present paper, we study the mixed summation integral type operators having Baskakov and Szász basis functions in summation and integration form, respectively. We also give here the alternate form of the operators in terms of hypergeometric functions and estimated moments of these operators using hypergeometric series. In the last section, we present some results for operators related to convergence. [ABSTRACT FROM AUTHOR]

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In this paper we introduce and study a subclass of analytic functions for operators on a Hilbert space in the open unit disk U = {z ϵ C : |z| < 1}. We have established coefficient estimates, distortion theorem for this subclass, and also an application to operators based on fractional calculus for this class is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we have proved certain kinds of Tauberian theorems for Nörlund-Cesáro summability methods in m-normed space X in statistically sense. We give necessary and sufficient Tauberian condition for this method of summability, in statistically sense. Also, we prove that Tauberian theorems under these summability methods are valid under oscillating slow condition of Schmidt-type and Hardy-type conditions. [ABSTRACT FROM AUTHOR]

Sensitivity analysis for cocoercively monotone variational inclusions based on the generalized resolvent operator technique is discussed. The notion of the cocoercive monotonicity unifies most of the existing notions, such as cocoercivity, strong monotonicity, relaxed monotonicity, relaxed cocoercivity, and others. As a result, the obtained results are general in nature. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the Bezier variant of modified Szasz-Mirakyan operators for functions of bounded variation. Our result extend and improve the results due to Sahai and Prasad [ Publ. Inst. Math. N.S.53(1993),73-80 ] and Gupta and Pant [ J. Math. Anal Appl. 233(1999),476-483]. [ABSTRACT FROM AUTHOR]

Abstract: In the case that a frame is prescribed for applications and erasures occur in the process of data transmissions, we examine optimal dual frames for the recovery from single erasures. In contrast to earlier papers, we consider the spectral radius of the error operator instead of its operator norm as a measure of optimality. This notion of optimality is natural when the Neumann series is used to recover the original data in an iterative manner. We obtain a complete characterization of spectrally one-erasure optimal dual frames in terms of the redundancy distribution of the prescribed frame. Our characterization relies on the connection between erasure optimal frames and the linear connectivity property of the frame. We prove that the linear connectivity property is equivalent to the intersection dependent property, and is also closely related to the well-known concept of a k-independent set. Additionally, we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iterative reconstruction work. [Copyright &y& Elsevier]