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J.P. King constructed a sequence of positive linear operators on C[0, 1] preserving the constant function 1 and the monomial x2. After that, several papers were devoted to positive linear operators preserving prescribed functions. In 2009, J.M. Aldaz, O. Kounchev, H. Render modified the classical Bernstein operators to get new operators fixing 1 and x j for a given j 2 N. Our aim is to construct operators acting on functions defined on [0,1) and preserving 1 and x j. To this end we consider suitable modifications of the Post-Widder and Gamma operators. Using pointwise asymptotic relations for the moments we obtain convergence results for the sequences of operators. Moreover, we establish the associated Voronovskaja formulas. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the existence and uniqueness of pseudo S -asymptotically periodic mild solutions for a class of neutral fractional evolution equations with finite delay. We essentially use the fractional powers of closed linear operators, the semigroup theory and some classical fixed point theorems. Furthermore, we provide an example to illustrate the applications of our abstract results. [ABSTRACT FROM AUTHOR]

In the present paper, some direct and inverse theorems relating to a generalization of positive linear operators are given. Also some rates of weighted statistical convergence are computed by means of a weighted modulus of continiuty. [ABSTRACT FROM AUTHOR]

We show that by a simple modification of the Bernstein operators one can obtain a polynomial approximation of unbounded functions which admit an asymptote at an end point of the interval and we give a typical example. We define a certain modulus of continuity which allow to give a quantitative result for the degree of approximation and to make more explicit the class of functions which can be approximate. Finally we show that these operators could be transformed in order to obtain linear positive operators for approximation of functions on interval $ [0, \infty) $. The scheme used in this paper is applicable in more general cases. [ABSTRACT FROM AUTHOR]

In this paper we study local approximation properties of a higher order Kantorovich-type Szász–Mirakjan operator recently introduced by Sabancigil, Kara, and Mahmudov. We derive the complete asymptotic expansion for these operators. They generalize the Szász–Mirakjan operators of Kantorovich-type and approximate locally integrable functions satisfying a certain growth condition on the infinite interval $ {(}0,\infty) $. [ABSTRACT FROM AUTHOR]

In the present paper, the authors introduce and investigate two new subclasses of the function class B of bi-univalent analytic functions in an open unit disk U connected with a linear q-convolution operator. The bounds on the coefficients | c 2 | , | c 3 | and | c 4 | for the functions in these new subclasses of B are obtained. Relevant connections of the results presented here with those obtained in earlier work are also pointed out. [ABSTRACT FROM AUTHOR]

Let c=(Cn)n≥0$$ c={\left({C}_n\right)}_{n\ge 0} $$ be the Catalan sequence and T$$ T $$ a linear and bounded operator on a Banach space X$$ X $$ such 4T$$ 4T $$ is a power‐bounded operator. The Catalan generating function is defined by the following Taylor series: C(T):=∑n=0∞CnTn.$$ C(T):= \sum \limits_{n=0}^{\infty }{C}_n{T}^n. $$Note that the operator C(T)$$ C(T) $$ is a solution of the quadratic equation TY2−Y+I=0$$ T{Y}^2-Y+I=0 $$. In this paper, we define powers of the Catalan generating function C(T)$$ C(T) $$ in terms of the Catalan triangle numbers. We obtain new formulae that involve Catalan triangle numbers: the spectrum of c∗j$$ {c}^{\ast j} $$ and the expression of c−∗j$$ {c}^{-\ast j} $$ for j≥1$$ j\ge 1 $$ in terms of Catalan polynomials (∗$$ \ast $$ is the usual convolution product in sequences). In the last section, we give some particular examples to illustrate our results and some ideas to continue this research in the future. [ABSTRACT FROM AUTHOR]

In this paper, the study of linear canonical Hankel pseudo-differential operators has been extended to Sobolev-type spaces. Two versions of pseudo-differential operators involving linear canonical Hankel transformation are defined. We have shown that the pseudo-differential operators and composition of pseudo-differential operators are bounded in certain Sobolev-type spaces associated with linear canonical Hankel transformations. [ABSTRACT FROM AUTHOR]

In this paper, we develop some generalized Fredholm perturbation results for bounded linear operators acting on non-reflexive Banach spaces satisfying certain conditions. Furthermore, we investigate the stability of the generalized Schechter S-essential spectrum by means of the so-called generalized Fredholm index. This concept is introduced as a semigroup homomorphism satisfying certain properties. Some generalized Fredholm results for block operator matrices acting on a non-reflexive product of two Banach spaces are also developed. [ABSTRACT FROM AUTHOR]

Let r ≥ 3 be a positive integer and F q the finite field with q elements. In this paper, we consider the r-regular complete permutation property of maps with the form f = τ ∘ σ M ∘ τ - 1 where τ is a PP over an extension field F q d and σ M is an invertible linear map over F q d . When τ is additive, we give a general construction of r-regular CPPs for any positive integer r. When τ is not additive, we give many examples of regular CPPs over the extension fields for r = 3 , 4 , 5 , 6 , 7 and for arbitrary odd positive integer r. These examples are the generalization of the first class of r-regular CPPs constructed by Xu et al. (Des Codes Cryptogr 90:545–575, 2022). [ABSTRACT FROM AUTHOR]

In this paper we show that for a vector space Vd$V_d$ of dimension d$d$ there exists a linear map detS2:Vd⊗d(2d−1)→k$det^{S^2}:V_d^{\otimes d(2d-1)}\rightarrow k$ with the property that detS2(⊗1⩽i

In this paper, the operator spectrum theory is applied to study the general stabilisation issues for mean‐field stochastic Markov jump systems (MF‐SMJSs), where multiple delays, multiplicative noises and homogeneous Markov chain exist simultaneously. The innovative contributions are described as follows. On the one hand, a feasible model augmented strategy is adopted to transform the dynamics into an auxiliary delay‐free form. By introducing a delay‐dependent linear Lyapunov operator (DDLLO), the Lyapunov/spectrum stabilising conditions are constructed, which are both necessary and sufficient. On the other hand, in terms of spectral analysis technique, the notions of interval stabilisation and essential destabilisation are generalised to MF‐SMJSs for the first time. The necessary and sufficient stabilisation conditions are derived, respectively, which can be verified availably by LMI feasibility tests. To confirm the effectiveness of the theoretic results, two illustrative examples are included. [ABSTRACT FROM AUTHOR]

Due to their rich information, color images are frequently utilized in many different industries, but the network's security in handling their delivery of images must be taken into account. To improve the security and efficiency of color images, this paper proposed a color image encryption algorithm based on cross-spiral transformation and zone diffusion. The proposed algorithm is based on Chen's system and the piecewise linear chaotic map, and uses the chaotic sequences generated by them for related operations. Firstly, the R, G and B planes are extracted, and the spiral starting point of each plane is randomly selected by the chaotic sequence to implement the cross-spiral transformation. Secondly, the bit-level image matrix is constructed by the scrambled image matrix, and the bit-level chaotic matrix is constructed by the chaotic sequence. Finally, the three-dimensional matrix is divided into four zones by a dividing line, and partition diffusion is carried out to obtain the encrypted image. Simulation results and algorithm analyses indicate that the proposed algorithm has superior performance and can resist a wide range of attacks. [ABSTRACT FROM AUTHOR]

We characterise all linear maps A : R n × n → R n × n such that, for 1 ≤ p < n , P L p ∗ (R n) ≤ c ( A [ P ] L p ∗ (R n) + Curl P L p (R n) ) holds for all compactly supported P ∈ C c ∞ (R n ; R n × n) , where Curl P displays the matrix curl. Being applicable to incompatible, that is, non-gradient matrix fields as well, such inequalities generalise the usual Korn-type inequalities used e.g. in linear elasticity. Different from previous contributions, the results gathered in this paper are applicable to all dimensions and optimal. This particularly necessitates the distinction of different combinations between the ellipticities of A , the integrability p and the underlying space dimensions n, especially requiring a finer analysis in the two-dimensional situation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative linear maps. We study cohomology and one-parameter formal deformation theory of left BiHom-alternative algebras. Moreover, we study central and Tθ -extensions of BiHom-alternative algebras and their relationship with cohomology. Finally, we investigate generalized derivations and give some relevant results. [ABSTRACT FROM AUTHOR]

This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The necessity is also obtainable under some regularity or when the polyhedral set is further the domain of the solution mapping. We further discuss possible conditions for the necessity and consider the solution mapping of a linear complementarity problem with a Q0 matrix as an example. [ABSTRACT FROM AUTHOR]

In this paper, we define a new sequence of positive linear operators in two variables by combining Chlodowsky operators and Szász type operators via Sheffer polynomials. Further, we calculate basic estimates. In the next section, we investigate their rapidity of convergence and order of approximation. Morever, Local approximation results and global approximation results are studied in various functional spaces. [ABSTRACT FROM AUTHOR]

Feature Evolvable Stream Learning (FESL) has received extensive attentions during the past few years where old features could vanish and new features could appear when learning with streaming data. Existing FESL algorithms are mainly designed for simple datasets with low-dimension features, nevertheless they are ineffective to deal with complex streams such as image sequences. Such crux lies in two facts: (1) the shallow model, which is supported to be feasible for the low-dimension streams, fails to reveal the complex nonlinear patterns of images, and (2) the linear mapping used to recover the vanished features from the new ones is inadequate to reconstruct the old features of image streams. In response, this paper explores a new online learning paradigm: Feature Evolvable Learning with Image Streams (FELIS) which attempts to make the online learners less restrictive and more applicable. In particular, we present a novel ensemble residual network (ERN), in which the prediction is weighted combination of classifiers learnt by the feature representations from several residual blocks, such that the learning is able to start with a shallow network that enjoys fast convergence, and then gradually switch to a deeper model when more data has been received to learn more complex hypotheses. Moreover, we amend the first residual block of ERN as an autoencoder, and then proposed a latent representation mapping (LRM) approach to exploit the relationship between the previous and current feature space of the image streams via minimizing the discrepancy of the latent representations from the two different feature spaces. We carried out experiments on both virtual and real scenarios over large-scale images, and the experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May and we study some of their approximation properties for different classes of continuous functions. First, we estimate the error of approximation in terms of the usual modulus of continuity and the second-order modulus of Ditzian and Totik. Then, we characterize the bounded functions that can be approximated uniformly by these new operators. In the last section, we obtain the most important results of the paper. We give the complete asymptotic expansion for the operators and we deduce a Voronovskaya-type theorem, results that hold true for smooth functions with exponential growth. [ABSTRACT FROM AUTHOR]

Because of the connection constraints of quantum devices, the quantum gate cannot operate directly on nonadjacent qubits. Quantum circuit mapping transforms a logical quantum circuit to a circuit that satisfies the connection constraints by adding SWAP gates for nonadjacent qubits. Global and local heuristic reordering strategies are proposed in this paper for quantum circuit mapping over linear nearest neighbor (LNN) architectures, which are one-dimensional topology structures, to reduce the number of SWAP gates added. Experiment results show that the average improvements of the two methods are 13.19% and 15.46%, respectively. In this paper, we consider the quantum circuit mapping problem for linear nearest neighbor (LNN) architectures. We propose a global heuristic qubit reordering optimization algorithm and a local heuristic qubit reordering optimization algorithm. Compared with the other algorithm results, the average improvements of the two methods for quantum cost are 13.19% and 15.46%, respectively. The two methods apply to the realization of quantum circuit neighboring over one-dimensional quantum architectures and can be extended to algorithms that work for other quantum architectures of different topologies. [ABSTRACT FROM AUTHOR]

In recent years, the study of robotic systems for agriculture, a modern research field often shortened as "precision agriculture", has become highly relevant, especially for those repetitive actions that can be automated thanks to innovative robotic solutions. This paper presents the kinematic model and a motion planning pipeline for a mobile manipulator specifically designed for precision agriculture applications, such as crop sampling and monitoring, formed by a novel articulated mobile base and a commercial collaborative manipulator with seven degrees of freedom. Starting from the models of the two subsystems, characterized by an adjustable position and orientation of the manipulator with respect to the mobile base, the linear mapping that describes the differential kinematics of the whole custom system is expressed as a function of the input commands. To perform pick–and–place tasks, a motion planning algorithm, based on the manipulator manipulability index mapping and a closed form inverse kinematics solution is presented. The motion of the system is based on the decoupling of the base and the arm mobility, and the paper discusses how the base can be properly used for manipulator positioning purposes. The closed form inverse kinematics solution is also provided as an open-source Matlab code. [ABSTRACT FROM AUTHOR]

In this paper, following the concept of AI-statistical convergence for real sequences introduced by Savas et al. [22], we deal with Korovkin type approximation theory for a sequence of positive convolution operators deĄned on C[a, b], the space of all real valued continuous functions on [a, b], in the line of Duman [6]. In the Section 3, we study the rate of AI-statistical convergence. [ABSTRACT FROM AUTHOR]

This paper continues the author's research on the problem of preserving the solvability of controlled operator equations. As a preliminary result (which is of independent interest) for a general operator acting on an arbitrary Banach space , new theorems on the existence and uniqueness of a fixed point are obtained. Here the well-known concept of the cone norm is used: , where is, generally speaking, another Banach space semi-ordered by the cone . These theorems are based on the assumption that the operator analog of the local Lipschitz condition with respect to the cone norm is satisfied and generalize the result by A.V. Kalinin and S.F. Morozov ( , ). The role of an analog of the Lipschitz constant on a given bounded set is played by a bounded linear operator , depending on this set, with spectral radius . In addition, M.A. Krasnosel'skii's lemmas on the equivalent norm are used. Based on the statements obtained, we prove theorems on local and total (over the set of admissible controls) preservation of the solvability of the controlled operator equation , , where is the control parameter from, generally speaking, an arbitrary set . The abstract theory is illustrated by examples of a controlled nonlinear operator differential equation in a Banach space as well as a strongly nonlinear pseudoparabolic equation. [ABSTRACT FROM AUTHOR]

The high-precision parameters in distribution networks are difficult to obtain, which brings difficulties to the model-based methods and analysis. With the widespread deployment of high-precision measurement units, data-driven methods have greater advantages in practice. In addition, with massive integration of distributed renewable generation and fast electric vehicle chargers, the fluctuations of net load increase significantly. The data-driven power flow calculation method based on the linear model becomes difficult to obtain accurate results for the low nonlinear adaptability. To improve the data-driven power flow calculation accuracy under high penetration of renewable distribution generation, this paper proposed an approach with high adaptability to the nonlinearity of power flow. Based on the thought of Koopman operator theory, the nonlinear relationship in power flow calculation is converted into a linear mapping in a higher dimension state space, which can significantly improve the calculation accuracy. Case studies on different IEEE cases have demonstrated that the proposed method can realize higher accuracy in power flow calculation with large-scale power fluctuations, compared to the existing data-driven method, in both mesh and radial networks. Finally, measurement data of a practical 10kV distribution network has been further used to verify the effectiveness of the proposed method in practical applications. [ABSTRACT FROM AUTHOR]

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let (X , ≤) be a locally finite pre-ordered set and R be a commutative ring with unity. In this paper we apply the theory of zero product determined algebras to show that each linear map on the incidence algebra I (X , R) which is derivable at zero is a generalized derivation and every local derivation on I (X , R) is a derivation. [ABSTRACT FROM AUTHOR]

In his recent Proceedings of the AMS paper, ''Gossez's skew linear map and its pathological maximally monotone multifunctions'', Stephen Simons proved that the closure of the range of the sum of the Gossez operator and a multiple of the duality map is not convex whenever the scalar is between 0 and 4. The problem of the convexity of that range when the scalar is equal to 4 was explicitly stated. In this paper, we answer this question in the negative for any scalar greater than or equal to 4. We derive this result from an abstract framework that allows us to also obtain a corresponding result for the Fitzpatrick-Phelps integral operator. [ABSTRACT FROM AUTHOR]

Although high dynamic range (HDR) display has become popular recently, the legacy content such as standard dynamic range (SDR) video is still in service and needs to be properly converted on HDR display devices. Therefore, it is desirable for HDR TV sets to have the capability of automatically converting input SDR video into HDR video, which is called reverse tone mapping (RTM). In this paper, we propose a novel learning-based low-complexity RTM scheme that not only expands the suppressed dynamic ranges (DR) of the SDR videos (or images), but also effectively restores lost detail in the SDR videos. Most existing conventional RTM schemes have focused on how to expand the DR of global contrast, resulting in limitations in recovering lost detail of SDR videos. On the other hand, the recent convolutional neural network-based approaches show promising results, but they are too complex to be applied on the users’ devices in practice. In this paper, our learning-based RTM scheme is computationally simple but effective in recovering lost detail. To learn the SDR-to-HDR relation, training “SDR-HDR” images are first separated into their base layer components and detail layer components by applying a guided filter. The detail layer components of the “SDR-HDR” pairs are used to train the SDR-to-HDR mapping. The mapping matrices are computed based on kernel ridge regression. In the meantime, the global contrast of the base layers is expanded by a nonlinear function that suppresses darker regions and amplifies brighter regions to fit the full DR of a target HDR display. To verify the effectiveness of our learning-based RTM scheme, we performed subjective quality assessment for images and videos. The experimental results show that our RTM scheme outperforms the existing RTM scheme with the successful restoration of lost detail in SDR images. [ABSTRACT FROM AUTHOR]

This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to ill-posedness of the inverse problems, conventional numerical approach for solutions results in arbitrarily large errors in solution. However, in the field of engineering mathematics, there are famous mathematical algorithms to tackle the ill-posed problem, which are known as regularization techniques. In the current study, a novel fractional Tikhonov regularization (NFTR) method is proposed to perform an effective inverse identification, then the smoothing functional of the ill-posed problem processed by the proposed method is regarded as an optimization problem, and finally a stable optimal solution is obtained by using an improved super-memory gradient (ISMG) method. The result of the present method is compared with that of the standard TR method and FTR method; new findings can be obtained; that is, the present method can improve accuracy and stability of the inverse identification problem, robustness is stronger, and the rate of convergence is faster. The applicability and efficiency of the present method in this paper are demonstrated through a mathematical example and an engineering example. [ABSTRACT FROM AUTHOR]

In this paper, we show that the maximum number of bent component functions of a vectorial function F:GF(2)^n\to GF(2)^n is 2^n-2^n/2 . We also show that it is very easy to construct such functions. However, it is a much more challenging task to find such functions in polynomial form F\in GF(2^n)[x] , where F has only a few terms. The only known power functions having such a large number of bent components are x^{d} , where d=2^{n/2}+1 . In this paper, we show that the binomials F^i(x)=x^2^i(x+x^2^n/2) also have such a large number of bent components, and these binomials are inequivalent to the monomials x^2^n/2+1 if 0

The goal of this paper is to establish a more generalized Cameron–Storvick theorem with respect to the conditional generalized integral transform (CGIT) and the generalized first variation. Many results and formulas for Cameron–Storvick theorems established in previous papers are included. We first introduce a CGIT and a generalized first variation of functionals by using the concept of the Gaussian process and bounded linear operators. We then give the existence of them for the exponential functionals on function space. We next establish a generalized Cameron–Storvick theorem. Finally, we describe some applications. [ABSTRACT FROM AUTHOR]

We show two more approaches for generating trajectory-based dynamics in the phase space formulation of quantum mechanics: 'equilibrium continuity dynamics' (ECD) in the spirit of the phase space continuity equation in classical mechanics, and 'equilibrium Hamiltonian dynamics' (EHD) in the spirit of the Hamilton equations of motion in classical mechanics. Both ECD and EHD can recover exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Both ECD and EHD conserve the quasi-probability within the infinitesimal volume dxtdpt around the phase point (xt, pt) along the trajectory. Numerical tests of both approaches in the Wigner phase space have been made for two strongly anharmonic model problems and a double well system, for each potential auto-correlation functions of both linear and nonlinear operators have been calculated. The results suggest EHD and ECD are two additional potential useful approaches for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]

For a fixed integer n≥2, let Mn be the algebra of all n × n matrices over the complex field C. Let x1,x2∈Cn be two fixed nonzero vectors, and fix also y1,y2∈Cn. In this paper, we characterize linear bijective maps φ:Mn→Mn having the property that φ(A)φ(B)x2=y2 whenever ABx1=y1. [ABSTRACT FROM AUTHOR]

In [1] (Kikete Wabuya, Luketero Wanyonyi, and Justus Mile) show that if an operator (n,m) hyponormal is isometrically equivalent to an operator S, then S is also (n,m) hyponormal operator. In this paper, we prove results in the same spirit but in a semi Hilbertian space, i.e., spaces generated by positive semi-definite sesquilinear forms. This kind of spaces appears in many problems concerning linear and bounded operators on Hilbert spaces and is intensively studied in the present; some of the basic properties of this class are studied. Moreover, the product, tensor product and the sum of finite numbers of this type are discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the algebraic and analytic q-de Rham complexes attached to linear q-difference operators with Laurent polynomial coefficients over the field of complex numbers. There is a natural morphism from the former to the latter complex. Whether or not it is a quasi-isomorphism, i.e. , whether or not the induced morphisms on the corresponding cohomology spaces are isomorphisms, is the basic question considered in the present paper. We study this question following three distinct approaches. The first one is based on duality, and leads to a direct connection between the problem considered in the present paper and the convergence of formal series solutions of q-difference equations. The second approach is sheaf theoretic, based on growth considerations. The third one relies on the local analytic theory of q-difference equations. The paper ends with an extension of our results to variants of the above q-de Rham complexes when certain q-spirals of poles are allowed. Our study includes the case |q| = 1. [ABSTRACT FROM AUTHOR]

In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et al. (Numer Math 145:915–971, 2020. https://doi.org/10.1007/s00211-020-01131-1), where it is shown that in such a setting the Laplace approximation error in Hellinger distance converges to zero in the order of the noise level. Here, we prove novel error estimates for a given noise level that also quantify the effect due to the nonlinearity of the forward mapping and the dimension of the problem. In particular, we are interested in settings in which a linear forward mapping is perturbed by a small nonlinear mapping. Our results indicate that in this case, the Laplace approximation error is of the size of the perturbation. The paper provides insight into Bayesian inference in nonlinear inverse problems, where linearization of the forward mapping has suitable approximation properties. [ABSTRACT FROM AUTHOR]

In this paper, we define the notions of trace pseudo-spectrum, ε--determinant spectrum and ε--trace of bounded linear operator pencils on non-Archimedean Banach spaces. Many results are proved about trace pseudo-spectrum, ε--determinant spectrum and ε--trace of bounded linear operator pencils on non-Archimedean Banach spaces. Examples are given to support our work. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematics, Mechanics & Computer Science is the property of Al-Farabi Kazakh National University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelastic type material and an elastic solid. To this end, we first derive the system of equations governing the deformations of such material. We give the suitable assumptions to obtain an existence and uniqueness result. The semigroups theory of linear operators is used. The paper concludes by proving the exponential decay of solutions with the help of a characterization of the exponentially stable semigroups of contractions and introducing an extra assumption. The impossibility of location is also shown. [ABSTRACT FROM AUTHOR]

In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in ℝ which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schrödinger operators. Motivated by their works, we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, all super-skewsymmetric super-biderivations of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are determined. It is shown that all the super-biderivations are inner. Furthermore, the linear super-commuting maps of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are standard. [ABSTRACT FROM AUTHOR]

In this paper, we give new results on demicompact linear operators, study some properties and some results on Fredholm and upper semi-Fredholm relations involving demicompact operators. Our results are used to provide a fine description of the essential pseudospectra. [ABSTRACT FROM AUTHOR]

For field development and drilling decisions, production assets and reservoir engineers require dynamic reservoir properties, such as saturation and pressure changes of a reservoir from the pre‐production virgin state. To date, geophysicists have produced time‐lapse (4D) seismic attributes (mostly on stacked seismic data) rather than dynamic parameters directly. In this paper, we present a new method to estimate saturation and pressure properties from time‐lapse seismic data to provide to reservoir engineers. This new three‐step method is demonstrated over the Edvard Grieg field in the North Sea. We can realize this method thanks to advanced seismic multi‐component acquisition via PP and PS seismic data and processing that allows accurate estimation of amplitude‐variation‐with‐offset parameters P‐ and S‐impedances. With time‐lapse P‐ and S‐impedances optimally resolved, we estimate a stable set of axes identifying water saturation increase (water replacing oil), gas saturation increase (gas injection or gas out of solution), pressure increase (at injectors) and pressure decrease (at producers). Once these axes are obtained, we convert every 4D P‐ and S‐impedance data points into 4D pseudo‐saturation and pseudo‐pressure using a transformation of coordinates. We next use the rock physics relationships of this field to show that a linear relationship can be used to map any 4D change in the field from impedances to saturations and pressures. Key locations in the field with largest saturation and pressure changes are used to find calibration values at these extreme points. Next, from the pseudo‐seismic 4D data, a linear mapping is used to calculate actual reservoir property changes (fractions for saturation and bars for pressure). This allows us to obtain fieldwide dynamic values for water and gas saturations and injection and production related pressure changes. The results are shown, and dynamic changes are interpreted on the Edvard Grieg field data. [ABSTRACT FROM AUTHOR]

In this paper, a novel Model Predictive Control (MPC) technique for multi-satellite formation flying geometry acquisition and maintenance in high-drag environment is presented. The proposed MPC relies on a linearized and convexified quasi-nonsingular Relative Orbital Elements (ROE) model based on state transition matrices propagation, allowing to include the effect of perturbations in the prediction to optimize fuel efficiency and tracking accuracy. The formation is controlled with respect to a non-decaying orbiting point to perform absolute and relative station keeping simultaneously. For this purpose, a new dedicated plant matrix to include drag effects on ROE in the propagation is derived and validated with respect to numerical results. In all simulations, the satellites are assumed to be equipped with a single low-thrust propulsion unit, therefore, specific constraints are included in the controller to obtain a feasible solution in a real operational scenario. Moreover, a collision avoidance constraint is added in case of close proximity operations exploiting a linear mapping between the set of ROE and cartesian coordinates expressed in the Local-Vertical-Local-Horizontal (LVLH) reference frame. The controller response is simulated in several realistic mission contexts with a high-fidelity orbital propagator and the results are validated for fuel efficiency by comparing them to similar approaches available in literature and to optimal solutions obtained respectively with a direct single shooting algorithm and with a closed-form impulsive formulation. [ABSTRACT FROM AUTHOR]

In the paper we deal with a time optimal control problem for a class of evolutionary equations involving two linear operators and a bilinear operator. Based on the existence and uniqueness of the solution, we establish the existence of optimal controls and several optimality conditions for the time optimal control problem. Finally, the main results are applied to a class of quasistatic frictional contact problems. [ABSTRACT FROM AUTHOR]