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In this paper, we investigate and study the notions of statistical product convergence and statistical product summability via deferred Cesàro and deferred Norlund product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two beautiful and definitively useful concepts. Also, based upon our proposed ideas, we demonstrate new thoughtful approximation of Korovkin-type theorems for a martingale sequence over a Banach space. Moreover, we establish that our theorems effectively extend and improve most (if not all) of the previously existing outcomes (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale sequences of random variables via deferred Cesaro ` mean. We then establish an inclusion theorem concerning the relation between these two beautiful and potentially useful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale sequence over a Banach space. Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are stronger than their traditional and statistical versions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate and study the concepts of statistical product convergence and statistical product summability via deferred Cesàro and deferred weighted product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two nice and potentially useful concepts. Also, based upon our proposed concepts, we state and prove a set of new Korovkin‐type approximation theorems for a martingale sequence over a Banach space. Moreover, we demonstrate that our approximation theorems effectively extend and improve most (if not all) of the previously existing results (both in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature. We also suggest a direction for future researches on this subject, which are based upon the basic (or q‐) calculus, but not upon the trivial and inconsequential variations involving the so‐called (p, q)‐calculus. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale difference sequences of random variables via deferred weighted summability mean. We then establish an inclusion theorem concerning the relation between these two beautiful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale difference sequence over a Banach space and demonstrate that our theorems effectively extend and improves most (if not all) of the previously existing results (in statistical and classical versions). Finally, we present an illustrative example by using the generalized Bernstein polynomial of a martingale difference sequence in order to demonstrate that our established theorems are stronger than its traditional and statistical versions. [ABSTRACT FROM AUTHOR]

We generalize and solve a problem regarding the divisibility of a sequence defined as the lower integer part of powers of the largest root of a polynomial equation. Two solutions are presented using various root finding, root extraction as well as algebraic techniques. We rely on the periodic properties of linear recurrences and powers of integers modulo primes and apply methods for estimating power sums and for determining limit points of the fractional part of powers of the largest root. We also present examples and discuss numerical and computational concerns. [ABSTRACT FROM AUTHOR]

The feasibility of efficient population transfer between an initial state and a decaying target state of the same parity without populating an intermediate state, in the presence of large-amplitude stochastic energy level fluctuations that mimic the dephasing in a solute molecule due to the influence of a solvent, is demonstrated theoretically. In particular, it is shown that a decaying target state, whose decay rate constant is large compared with the band width of picosecond laser pulses but small compared with the associated peak Rabi frequencies, can dramatically suppress the dephasing-induced nonadiabaticity associated with the dynamics of population transfer, resulting in, irrespective of the correlation time of stochastic energy level fluctuations, negligible population in the intermediate state and complete population transfer to the decaying target state. These results should further motivate experimental studies of optical control of molecular dynamics in a liquid. An interesting connection between our results and the quantum Zeno and anti-Zeno effects is also discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper presents a study of using a genetic algorithm (GA) method to select the machining operation sequence for prismatic parts. Four types of process planning rules including precedence rules, clustering rules, adjacent order rules and optimization rules are considered and are encompassed quantitatively in the fitness calculations for alternative operation sequences. The impact of variations of the rules on the result of operation sequencing and that of GA parameters on the solution efficiency are discussed through analysis of examples and experiments. The proposed genetic algorithm proves effective for machining operation sequencing of prismatic parts, by incorporating various production environment considerations into process planning. [ABSTRACT FROM AUTHOR]

A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twisted n‐layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials. [ABSTRACT FROM AUTHOR]

Abstract Let G be a multiplicative finite group and S = a 1 ⋅ ... ⋅ a k a sequence over G. We call S a product-one sequence if 1 = ∏ i = 1 k a τ (i) holds for some permutation τ of { 1 , ... , k }. The small Davenport constant d (G) is the maximal length of a product-one free sequence over G. For a subset L ⊂ N , let s L (G) denote the smallest l ∈ N 0 ∪ { ∞ } such that every sequence S over G of length | S | ≥ l has a product-one subsequence T of length | T | ∈ L. Denote e (G) = max ⁡ { ord (g) : g ∈ G }. Some classical product-one (zero-sum) invariants including D (G) : = s N (G) (when G is abelian), E (G) : = s { | G | } (G) , s (G) : = s { e (G) } (G) , η (G) : = s [ 1 , e (G) ] (G) and s d N (G) (d ∈ N) have received a lot of studies. The Noether number β (G) which is closely related to zero-sum theory is defined to be the maximal degree bound for the generators of the algebra of polynomial invariants. Let G ≅ C m ⋉ φ C m n , in this paper, we prove that E (G) = d (G) + | G | = m 2 n + m + m n − 2 and β (G) = d (G) + 1 = m + m n − 1. We also prove that s m n N (G) = m + 2 m n − 2 and provide the upper bounds of η (G) , s (G). Moreover, if G is a non-cyclic nilpotent group and p is the smallest prime divisor of | G | , we prove that β (G) ≤ | G | p + p − 1 except if p = 2 and G is a dicyclic group, in which case β (G) = 1 2 | G | + 2. [ABSTRACT FROM AUTHOR]

In 2001, Kennedy et al. [Amer. Math. Mon. 108, 411–423 (2001) and Trans. Amer. Math. Soc. 353, 2513–2530 (2001)] showed a chaos lemma and stated the pseudoconjecture "stretches across implies existence of an invariant set." In this paper, we give a suitable definition of stretches across in topological sense so that the conjecture has an affirmative answer. More precisely, we show that there must be an orbit through a sequence of stretches across. In particular, a closed loop of stretches across implies existence of a periodic orbit. We also give the geometric meaning of stretches across and its relation with the global implicit function theorem. [ABSTRACT FROM AUTHOR]

Abstract We propose a new greedy Kaczmarz algorithm for the solution of very large systems of linear equations. In our proposed algorithm, control sequence is determined by a greedy rule, and relaxation parameters are determined adaptively. Convergence of our proposed algorithm is proved. Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm. [ABSTRACT FROM AUTHOR]

Abstract In the present paper, we consider the discrete nonlinear Schrödinger equation − Δ u n + v n u n − ω u n = γ g n (u n) + h n , n ∈ Z , where v n , h n are real valued sequences, ω ∈ R , γ = ± 1 , and g n is a function sequence. We study this non-periodic discrete nonlinear Schrödinger equation with infinitely growing potential. Under some suitable conditions, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. It is the first time to investigate the nonhomogeneous discrete nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of estimating the local strain tensor from a sequence of micro-structural images realized during deformation tests of engineering materials. Since the strain tensor is defined via the Jacobian of the displacement field, we propose to compute the displacement field by a variational model which takes care of properties of the Jacobian of the displacement. In particular, we are interested in areas of high strain. The data term of our variational model relies on the brightness invariance property of the image sequence. As prior we choose the second order total generalized variation of the displacement field. This splits the Jacobian into a smooth and a non-smooth part. The latter reflects the material cracks. An additional constraint is incorporated to handle physical properties of the non-smooth part for tensile tests. We prove that the resulting convex model has a minimizer and show how a primal-dual method can be applied to find a minimizer. The corresponding algorithm has the advantage that the strain tensor is directly computed within the iteration process. It is further equipped with a coarse-to-fine strategy to cope with larger displacements. Numerical examples with simulated and experimental data demonstrate the very good performance of our algorithm. In comparison to state-of-the-art engineering software, our method can resolve local phenomena much better. [ABSTRACT FROM AUTHOR]

Abstract We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights (γ j) j ≥ 1 under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires sup d ≥ 1 max 0̸ ≠ u ⊆ [ d ] ∏ j ∈ u (j γ j) < ∞. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy. [ABSTRACT FROM AUTHOR]

We introduce double λ -statistically convergent sequences and double λ -statistically Cauchy sequences in the fuzzy normed spaces. We study [V,ë ]- and [C,1]-summabilities for double sequences. In addition, we obtain the relation between these concepts and λ -statistically convergence. [ABSTRACT FROM AUTHOR]

Abstract We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using " t -spanning" routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t -spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an efficient method for constructing 2 2 n − 2 cyclic different de Bruijn sequences of order 2 n from the feedback function of a de Bruijn sequence of order n. This is done by extending an n -stage nonlinear feedback shift register (NFSR) to a 2 n -stage NFSR, and then recursively joining all cycles of the 2 n -stage NFSR to form a full cycle. [ABSTRACT FROM AUTHOR]

We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time-space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Stochastic RF excitation and resulting data correlation before image reconstruction. • Use of stochastic sequences can result in reduced RF power during EPR imaging. • Reduced RF power brings the SAR of EPR imaging near levels of some MRI imaging. • SAR levels are low enough to explore possible clinical applications. Abstract An excessive RF power requirement is one of the main obstacles in the clinical translation of EPR imaging. The radio frequency (RF) pulses used in EPR imaging to excite electron spins must be very short to match their fast relaxation. With traditional pulse schemes and ninety degree flip angles, this can lead to either unsafe specific absorption rate (SAR) levels or unfeasibly long repetition times. In spectroscopy experiments, it has been shown that stochastic excitation and correlation detection can reduce the power while maintaining sensitivity but have yet to be applied to imaging experiments. Stochastic excitation is implemented using a pseudo-random phase modulation of the input stimulus. Using a crossed coil resonator assembly comprised of an outer saddle coil and an inner surface coil, it was possible to obtain a minimum isolation of ∼50 dB across a 12 MHz bandwidth. An incident peak RF power of 5 mW was used to excite the system. The low background signal obtained from this resonator allowed us to generate images with 32 dB (>1000:1) signal-to-noise ratio (SNR) while exciting with a traditional pulse sequence in a phantom containing the solid paramagnetic probe NMP-TCNQ (N-methyl pyridinium tetracyanoquinodimethane). Using two different stochastic excitation schemes, we were able to achieve a greater than 4-fold increase in SNR at the same peak power and number of averages, compared to single pulse excitation. This procedure allowed imaging at significantly lower RF power levels than used in conventional EPR imaging system configurations. Similar techniques may enable clinical applications for EPR imaging by facilitating the use of larger RF coils while maintaining a safe SAR level. [ABSTRACT FROM AUTHOR]

We prove that the solutions to the k -peg Tower of Hanoi problem given by Frame and Stewart are minimal. The proof relies on first identifying that for any n -disk, k -peg problem, there is at least one minimal sequence is symmetric. We show that if we order the number moved required for the disks in the minimal symmetric sequence in an increasing manner and obtain the sequence x i , then x i ≥ 2 i − 1 . We also prove that the maximum number of disks that can be moved using x i steps is k − 4 + i k − 3 . We use these to lower bound the telescopic sum (2) that is a lower bound on the number of moves required for any minimal symmetric sequence. This gives us the required result. [ABSTRACT FROM AUTHOR]

The effects of nonlinear dynamical phenomena on strategies for creating large amplitude excitations in molecular systems are studied. A simple area-preserving mapping modeling a Morse oscillator coupled to a second intramolecular degree of freedom is considered. The optical field is approximated by a finite sequence of impulsive interactions with arbitrary amplitudes and time increments. The goal of exciting the system to 75% of its dissociation energy is established. For the uncoupled Morse oscillator, an analytic solution for the optimal spacing between pulses of minimal equal intensity is given. When intramolecular coupling is present, the existence of a nonlinear resonance zone is shown to strongly interfere with the efficacy of this strategy. Dramatic improvements in efficiency can be obtained by employing pulse sequences that explicitly take into account the presence of strong perturbations of the zeroth order phase portrait. [ABSTRACT FROM AUTHOR]

We extend an intuitive level part usage measure to the multi-level case, and provide a practical yet powerful algorithm The measure assigns an ideal due-date to each unit of each part type of each level, and sums the squared deviation between these ideal due-dates and the actual completion times. The algorithm schedules the final products in earliest ideal due-date order. This algorithm entirely ignores the lower levels and is consequently extremely fast. Surprisingly, in addition to being many times faster than other algorithms, this quick and dirty algorithm performs very well with respect to both the new ideal due-date measure, and the multi-level goal-chasing measure. [ABSTRACT FROM AUTHOR]

Photomatrix therapeutic systems (PMTS) are widely used for the tasks of preventive, stimulating and rehabilitation medicine. They consist of low-intensity light-emitting diodes (LEDs) having the quasi-monochromatic irradiation properties. Depending on the LED matrix structures, PMTS are intended to be used for local and large areas of bio-objects. However, in the case of non-uniform irradiation of biological tissues, there is a risk of an inadequate physiological response to this type of exposure. The proposed approach considers a novel technique for designing this type of biomedical technical systems, which use the capabilities of stochastic algorithms for LED switching. As a result, the use of stochastic photomatrix systems based on the technology of uniform twisting generation of random variables significantly expands the possibilities of their medical application.

Let G be a sofic group, and let Σ = (σn)n #8805;1 be a sofic approximation to it. For a probability-preserving G-system, a variant of the sofic entropy relative to Σ has recently been defined in terms of sequences of measures on its model spaces that 'converge' to the system in a certain sense. Here we prove that, in order to study this notion, one may restrict attention to those sequences that have the asymptotic equipartition property. This may be seen as a relative of the Shannon-McMillan theorem in the sofic setting. We also give some first applications of this result, including a new formula for the sofic entropy of a (G x H)-system obtained by co-induction from a G-system, where H is any other infinite sofic group. [ABSTRACT FROM AUTHOR]

Abstract On the basis of the order in which twinning occurs, twins are termed primary, secondary, and tertiary. In HCP materials, compression twins (CT) and extension twins (ET) are observed to form alternatively during sequential twinning. However, selections of twinning systems and variants are not yet fully understood. Both ET→CT→ET and CT→ET→CT sequences have been reported in literatures. Here we conduct a systematic and statistical study on the evolutions of twinning sequences and variants during cryogenic rolling of Ti. Both twinning sequences are observed in the same sample. Current statistical results indicate the selections of the twinning sequence and variants are governed by the following criteria: (1) the twinning sequence in an individual grain depends on its initial orientation; (2) the twin variant selection is mainly governed by the Schmid's law, although a few non-Schmid twins are observed along the short axis of the parent grains. These criteria are thought applicable to other HCP metallic materials. Highlights • Both ET→CT→ET and CT→ET→CT twining sequences were found in a LNT-rolled Ti sample. • Grain orientation dominates twinning systems variation in twinning sequence. • Schmid law can primarily explain the twin variant selection in twinning sequence. • The formation of low Schmid factor twin could be attributed to the low twinning free path. [ABSTRACT FROM AUTHOR]

We study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a countable intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to introduce new notions, namely, Wijsman asymptotically I2-statistical equivalence of weight g, Wijsman strongly asymptotically I2-lacunary equivalence of weight g and Wijsman asymptotically I2-lacunary statistical equivalence of weight g of double set sequences. We mainly investigate their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

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Abstract We adapt and generalize to conservative systems the analysis of a model in Tartar (1989), a sequence of differential equations which in the limit gives an effective equation with a memory effect: our result is obtained under more realistic assumptions concerning the oscillations of the initial data and the coefficients. [ABSTRACT FROM AUTHOR]

We prove the quantum conditional entropy power inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional entropy power inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional entropy power inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogs of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on entropy power inequalities. [ABSTRACT FROM AUTHOR]

We define a class of ORV sequences with nondegenerate groups of regular points and consider some properties of these sequences. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A new method of stochastically excited NMR excites and receives broadband spectra. • Pulse blocks and acquire blocks are interleaved in a pseudo-random schedule. • Broad powder patterns are acquired with pulse powers of <1 mW. • The method will allow compact NMR instruments to acquire wideline spectra. Abstract Motivated by recent generations of compact portable and benchtop NMR instrumentation, we present a new method for the acquisition of broad bandwidth NMR spectra using stochastic excitation. The new method decouples the spectral width from the durations of the excitation pulses and ring-down delays, allowing the receiver bandwidth to be arbitrarily large. This allows low-power, low-flip-angle pulses to be used to acquire broad-band NMR spectra such as wideline powder patterns from solids. The new method divides experimental time into distinct "pulse" and "acquire" blocks that are interleaved according to a pseudo-random noise sequence and combined with a second sequence for phase modulation. The method is described mathematically, and is demonstrated with both liquids and wide-line solids experiments. [ABSTRACT FROM AUTHOR]

In this paper, statistical epi-limit is defined by using epigraphs in order to increase sensitivity by eliminating outliers for mathematical problems. Various characterizations of statistical epi-convergence and their relations are given and it is compared with statistical convergence. Also, its connections with level sets and monotone increasing or decreasing cases are studied. Moreover, statistical equi-lower semicontinuity and its relation with statistical epilimit is examined. [ABSTRACT FROM AUTHOR]

Martingale-like sequences in vector lattice and Banach lattice frameworks are defined in the same way as martingales are defined in [Positivity 9 (2005), 437-456]. In these frameworks, a collection of bounded X-martingales is shown to be a Banach space under the supremum norm, and under some conditions it is also a Banach lattice with coordinatewise order. Moreover, a necessary and sufficient condition is presented for the collection of E-martingales to be a vector lattice with coordinate-wise order. It is also shown that the collection of bounded E-martingales is a normed lattice but not necessarily a Banach space under the supremum norm. [ABSTRACT FROM AUTHOR]

This work focuses on the influence of a simple pole on a new function representing method we called separate node ascending derivatives expansion (SNADE) convergence characteristics. Even though SNADE can be somehow considered as a new Taylor series expansion, it is distincted from Taylor series expansion by its different nodal points using features. This paper focuses on certain details of SNADE about convergence and its validity. Beyond that, this research focusing on the influence of a simple pole location in the function on the convergence characteristics involves completely new original findings and reported in this paper where a specific importance is given to the case where the SNADE nodal sequence is composed of elements alternating between two nodal values. [ABSTRACT FROM AUTHOR]

A library of 16 digitally encoded polyanions was used in a layer‐by‐layer (LbL) polyelectrolyte assembly to nanofabricate thin films containing digitally coded strata. The polyanions were digital polyphosphodiesters (d‐PPDE) prepared via an automated phosphoramidite process. Each component of the library contained 10 bytes of ASCII‐encoded text (i.e. 80 coded monomers); thus the entire library allows the writing of a full sentence, which can be stored in a multilayer film as a sequence of sequences. To prepare fully segregated digital domains, non‐coded layers composed of poly(allylamine hydrochloride) (PAH)/poly(sodium 4‐styrenesulfonate) (PSS) were included between the d‐PPDE coded layers as an intermediate barrier. Detailed analysis of the film homogeneity indicated formation of 70 nm‐thick films in which digital layers are kept apart from another by non‐coded interlayers. As a result, the sequence‐coded polymer library could be piled‐up in a defined sequence of layers. Thin films containing segregated layers of digitally encoded polymers were prepared and characterized. An ASCII‐encoded sentence of 160 bytes was stored in these films using a library of 16 different digital polyanions. The results show that abiotic coded matter can be organized in precise nanoscale morphologies. [ABSTRACT FROM AUTHOR]

Gradient descent (GD) is a widely used optimization algorithm in machine learning. In this paper, a novel stochastic computing GD circuit (SC-GDC) is proposed by encoding the gradient information in stochastic sequences. Inspired by the structure of a neuron, a stochastic integrator is used to optimize the weights in a learning machine by its “inhibitory” and “excitatory” inputs. Specifically, two AND (or XNOR) gates for the unipolar representation (or the bipolar representation) and one stochastic integrator are, respectively, used to implement the multiplications and accumulations in a GD algorithm. Thus, the SC-GDC is very area- and power-efficient. As per the formulation of the proposed SC-GDC, it provides unbiased estimate of the optimized weights in a learning algorithm. The proposed SC-GDC is then used to implement a least-mean-square algorithm and a softmax regression. With a similar accuracy, the proposed design achieves more than $30 \times $ improvement in throughput per area (TPA) and consumes less than 13% of the energy per training sample, compared with a fixed-point implementation. Moreover, a signed SC-GDC is proposed for training complex neural networks (NNs). It is shown that for a 784-128-128-10 fully connected NN, the signed SC-GDC produces a similar training result with its fixed-point counterpart, while achieving more than 90% energy saving and 82% reduction in training time with more than $50 \times $ improvement in TPA. [ABSTRACT FROM AUTHOR]

We extend some results known from the literature for ordinary (single) sequences to multiple sequences of real numbers. Further, we introduce a concept of double lacunary strong (A, φ) -convergence with respect to a modulus function. In addition, we also study some relationships between double lacunary strong (A, φ) -convergence with respect to a modulus and double lacunary statistical convergence. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study triple difference sequence spaces over n-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established. [ABSTRACT FROM AUTHOR]

It is shown that bounded sequences satisfying nonlinear differential constraints, strongly precompact under an exact condition of nondegeneration of these conditions. The proof is based on new localization principles for ultraparabolic H-measures with continuous indices. [ABSTRACT FROM AUTHOR]

We study an iterative process to accelerate the successive approximations method in a monotonous convergence framework. It consists in interrupting the sequence of the successive approximations method produced at the kth iteration and substituting it by a combination of the element of the sequence produced at the iterate k + 1 and an extrapolation vector. The latter uses a parameter which can be calculated mathematically. We illustrate numerically this process by studying a free-boundary problems class. [ABSTRACT FROM AUTHOR]

Let ɷ ⊆ R² be a domain and let f ε W1,1(ɷ,R²) be a homeomorphism (between ɷ and f(ɷ)) Then there exists a sequence of smooth diffeomorphisms fk converging to f in W1,1(ɷ,R²) and uniformly. [ABSTRACT FROM AUTHOR]