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This paper studies the fractional quasi‐geostrophic equation with modified dissipation term. We first prove the existence and uniqueness of smooth solution of the fractional quasi‐geostrophic equation by using the regularization method. Then, utilizing the Fourier‐splitting method, we obtain the long‐time behavior of the solution. More precisely, we show that under suitable assumptions on the initial data, for any multi‐index γ,m≥4$$ \gamma, m\ge 4 $$ and α∈12,1$$ \alpha \in \left(\frac{1}{2},1\right) $$, the solution ψ$$ \psi $$ satisfies C1(1+t)−1+|γ|2+2α≤∇γψ(·,t)L2≤C2(1+t)−1+|γ|2+2α,|γ|=0,1,...,m−1,t≥1,$$ {C}_1{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }}\le {\left\Vert {\nabla}^{\gamma}\psi \left(\cdotp, t\right)\right\Vert}_{L^2}\le {C}_2{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }},\mid \gamma \mid =0,1,\dots, m-1,t\ge 1, $$and C3(1+t)−1+|γ|2+2α≤||∇γψ(·,t)||L2≤C4(1+t)−|γ|2+2α,|γ|=m,t≥1.$$ {C}_3{\left(1+t\right)}^{-\frac{1+\mid \gamma \mid }{2+2\alpha }}\le {\left\Vert {\nabla}^{\gamma}\psi \Big(\cdotp, t\Big)\right\Vert}_{L^2}\le {C}_4{\left(1+t\right)}^{-\frac{\mid \gamma \mid }{2+2\alpha }},\mid \gamma \mid =m,t\ge 1. $$ [ABSTRACT FROM AUTHOR]

AbstractThis paper presents new simple lower and upper bounds for the cumulative normal distribution function, Φ(z). The accuracy and closeness of the proposed bounds to the exact Φ(z) are investigated based on the maximum absolute error and the mean absolute error. It is found that the maximum absolute error of the proposed lower bound is 8.55×10−3 and it is 4.1×10−4 for the upper bound. In addition, based on 5001 values between z=0 and z=5 with step 0.001, we found that the mean absolute error is 3.27×10−3 for the lower bound and it is 1.1×10−4 for the upper bound and these two values decrease with increasing the z value. [ABSTRACT FROM AUTHOR]

We consider the eigenvalues of the magnetic Laplacian on a bounded domain Ω of R 2 with uniform magnetic field β > 0 and magnetic Neumann boundary conditions. We find upper and lower bounds for the ground state energy λ 1 and we provide semiclassical estimates in the spirit of Kröger for the first Riesz mean of the eigenvalues. We also discuss upper bounds for the first eigenvalue for non-constant magnetic fields β = β (x) on a simply connected domain in a Riemannian surface. In particular: we prove the upper bound λ 1 < β for a general plane domain for a constant magnetic field, and the upper bound λ 1 < max x ∈ Ω ‾ ⁡ | β (x) | for a variable magnetic field when Ω is simply connected. For smooth domains, we prove a lower bound of λ 1 depending only on the intensity of the magnetic field β and the rolling radius of the domain. The estimates on the Riesz mean imply an upper bound for the averages of the first k eigenvalues which is sharp when k → ∞ and consists of the semiclassical limit 2 π k | Ω | plus an oscillating term. We also construct several examples, showing the importance of the topology: in particular we show that an arbitrarily small tubular neighborhood of a generic simple closed curve has lowest eigenvalue bounded away from zero, contrary to the case of a simply connected domain of small area, for which λ 1 is always small. [ABSTRACT FROM AUTHOR]

We consider the motion of an incompressible shear-thickening power-law-like non-Newtonian fluid in R 3 with a variable power-law index. This system of nonlinear partial differential equations arises in mathematical models of electrorheological fluids. The aim of this paper is to investigate the large-time behaviour of the difference u - u ~ where u is a strong solution of the given equations with the initial data u 0 and u ~ is the strong solution of the same equations with perturbed initial data u 0 + w 0 . The initial perturbation w 0 is not required to be small, but is assumed to satisfy certain decay condition. In particular, we can show that (1 + t) - γ 2 ≲ ‖ u ~ (t) - u (t) ‖ 2 ≲ (1 + t) - γ 2 , for sufficiently large t > 0 , where γ ∈ (2 , 5 2) . The proof is based on the observation that the solution of the linear heat equation describes the asymptotic behaviour of the solutions of the electrorheological fluids well for sufficiently large time t > 0 , and the generalized Fourier splitting method with an iterative argument. Furthermore, it will also be discussed that the argument used in the present paper can improve the previous results for the generalized Newtonian fluids with a constant power-law index. [ABSTRACT FROM AUTHOR]

Integer ambiguity resolution (IAR) is one of the key techniques in GNSS high precise positioning. However, an overlooked incorrect integer ambiguity solution may cause severe biases in the positioning results. The optimal integer aperture estimator (IAE) has the largest possible success rate given a certain fail rate. An alternative approach that take advantage of ambiguity integer nature to minimize the solution’s mean squared error (MSE) is known as the best integer equivariant (BIE) estimator. Both of which are associated with the posterior probability of the GNSS integer ambiguity. It is therefore of great significance to calculate posterior probability precisely and efficiently. Due to the occurrence of infinite sums, practical calculation approaches approximate the exact value by neglecting sufficiently small terms in the sum. As a result, they can only produce posterior probability calculation result, information about the result’s accuracy cannot be produced. In this contribution, the value of the posterior probability is bounded from below and from above by dividing the infinite sum into two parts: the major finite part and the minor infinite part. They are calculated partly by enumeration and partly by algebraical bounding. The obtained upper and lower bounds are rigorous and in closed form, so that can be conveniently used. Based on both of the bounds, a method of posterior probability calculation with controllable accuracy is proposed. It not only produces posterior probability calculation result, but also calculation error, which is always smaller than the user-defined acceptable error. Numerical experiments have verified that the proposed approach has advantages on both controllable calculation accuracy and adjustable computational workload. [ABSTRACT FROM AUTHOR]

The paper deals with two general families of cumulative distribution functions based on arctangent function. We provide analysis of the error of the best one-sided Hausdorff approximation for some special cases of these families. We obtain precious estimates for the value of the Hausdorff distance that can be used as an additional criterion in practice. Further, the family of recurrence generated adaptive functions is constructed and investigated. All new results are illustrated with suitable numerical experiments. Simple dynamic software modules show applicability of Hausdorff approximation. [ABSTRACT FROM AUTHOR]

Considered herein is the global existence and non-global existence of the initial-boundary value problem for a quasilinear viscoelastic equation with strong damping and source terms. Firstly, we introduce a family of potential wells and give the invariance of some sets, which are essential to derive the main results. Secondly, we establish the existence of global weak solutions under the low initial energy and critical initial energy by the combination of the Galerkin approximation and improved potential well method involving with t. Thirdly, we obtain the finite time blow-up result for certain solutions with the non-positive initial energy and positive initial energy, and then give the upper bound for the blow-up time T*. Especially, the threshold result between global existence and non-global existence is given under some certain conditions. Finally, a lower bound for the life span T* is derived by the means of integro-differential inequality techniques. [ABSTRACT FROM AUTHOR]

In this paper, some new upper and lower bounds on the blow-up time of a certain class of nonlinear Volterra integral equations are presented and compared to previously proposed bounds. In most cases, the new bounds are a significant improvement on previously proposed bounds. We present many new bounds, with varying degrees of accuracy and computational complexity. The derivation of the upper bounds is made possible by a certain covariance inequality from advanced probability theory, which opens the door to many future investigations of blow-up time estimations in many other nonlinear integral equations. [ABSTRACT FROM AUTHOR]

Clay with free gas bubbles can be frequently encountered in the seabed. Gassy clay is an unsaturated soil, but its mechanical behavior cannot be described using conventional unsaturated soil mechanics because it has a composite internal structure with a saturated soil matrix and gas bubbles. The gas bubbles can have either a detrimental or beneficial effect on the undrained shear strength of clay. New lower and upper bounds for the undrained shear strength of gassy clay are derived by considering the effect of total stress path and plastic hardening of the saturated soil matrix. For the upper bound, it is assumed that there is only bubble flooding, and the shear strength of an unsaturated soil sample is the same as that of the saturated soil matrix. Bubble flooding makes the saturated soil matrix partially drained and increases the undrained shear strength. The amount of bubble flooding is calculated using the modified Cam-Clay model and Boyle's law for ideal gas. The lower bound is derived based on the assumption that the entire soil fails without bubble flooding and the gas cavity size evolves due to plastic hardening of the saturated soil matrix. Compared with Wheeler's upper and lower bounds that do not consider plastic hardening of the saturated soil matrix, the new theoretical results give a better prediction of the undrained shear strength of gassy clays, especially for the upper bound. Implications for constitutive modeling of gassy clay are discussed based on the new research outcomes. [ABSTRACT FROM AUTHOR]

Ambient backscatter communication (AmBC), a promising solution to future Internet of Things (IoT), has attracted increasing attention from both academia and industry in recent years. AmBC systems enable communications between RF-powered devices (e.g., tags and sensors) and AmBC receivers by utilizing ambient RF source signals from existing communication systems. Thus it offers a low-cost and energy-efficient means of communications for future IoT applications. In the current AmBC research, the impact of using channel coding on existing primary networks in terms of the bit-error-rate (BER) performance of the AmBC systems are mostly ignored. Low-density parity-check (LDPC) codes that offer fast encoding and decoding process have been proposed as promising channel codes in the fifth-generation (5 G) networks. In this paper, we investigate the BER performance of an AmBC system that uses LDPC-coded RF source signals. We have analytically derived the BER upper and lower bounds of both the RF source and tag signals for our proposed AmBC system. Simulation results show that the BERs of both signals decrease significantly, compared to conventional AmBC systems with uncoded RF source signals. [ABSTRACT FROM AUTHOR]

In this paper, some new upper bounds on the spectral radius of Hadamard product of nonnegative tensors are given. To show their sharpness, the comparisons among these bounds, including the existing one by Sun et al. (Linear Multilinear Algebra 66:1199–1214, 2018), are performed. We also present some lower bounds on the minimum eigenvalue of Fan product of irreducible strong M -tensors and their sharpness under different conditions are investigated. Some numerical examples are provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut-Δum = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions. Based on the auxiliary functions and differential-integral inequalities, the blow-up criterions which ensure that u cannot exist all time are given under two different assumptions, and the corresponding estimates on the upper bounds for blow-up time and blow-up rate are derived respectively. Moreover, we use three different methods to determine the lower bounds for blow-up time and blow-up rate estimates if blow-up does occurs. [ABSTRACT FROM AUTHOR]

In this note, we consider a constant c related to the Glaisher-Kinkelin constant, obtained by a shift of the infinite system of Equations for the Li-Keiper coefficients and related to the Euler formula at s = 2, i.e. ζ(2) = 2/6 for the Zeta function. The aim of the experiment we are carrying out is to relate the Primes with the tiny part (the fluctuations) of the Li-Keiper coefficients as well as with the trend part of them. The contribution of the series for the tiny part or for the trend part are thus related to a series for the primes and we obtain in this ways a upper and a lower bound of the constant c, which will be given with some decimals. Other relations may be obtained along the same lines and additional examples are given. [ABSTRACT FROM AUTHOR]

For visible light communication (VLC), the light signals are transmitted without optical fibers or any sort of wave-guiding. Due to the inherent broadcast nature, physical-layer security emerges as a promising method to protect information delivery from eavesdropping. As for the secrecy capacity of VLC channel, there exist two features. In one way, the limited optical power makes the common capacity expressions in radio-frequency (RF) communication unapplicable for VLC. In another way, several correlated geometrical parameters directly alters the Lambertian model of indoor VLC channel, which gives the secrecy capacity more meanings. However, the issue considering both aspects has not been studied recently. In this paper, from the practical scenarios, we extract a typical geometrical model to reveal the mobility principles of the legitimate receiver and the eavesdroppers. Then, we character two typical distributions of the geometrical parameter. Correspondingly, we derive the upper and lower bounds on the average secrecy capacity, which have the closed forms. Finally, simulation results show that our upper and lower bounds are tight at high optical signal-to-noise rates (OSNRs). Moreover, the geometrical features of VLC systems and distribution parameters of the receiver mobility are effectively reveal by the bounds. [ABSTRACT FROM AUTHOR]

In this paper, we present some new results on a class of tensors, which are defined by the solvability of the corresponding tensor complementarity problem. For such structured tensors, we give a sufficient condition to guarantee the nonzero solution of the corresponding tensor complementarity problem with a vector containing at least two nonzero components and discuss their relationships with some other structured tensors. Furthermore, with respect to the tensor complementarity problem with a nonnegative such structured tensor, we obtain the upper and lower bounds of its solution set, and by the way, we show that the eigenvalues of such a tensor are closely related to this solution set. [ABSTRACT FROM AUTHOR]

This study is concerned with the large time decay estimates for weak solutions of the surface quasi-geostrophic equation with H ˙ − 1 2 initial data. Due to some special observation together with applying the decay characters to the class of H ˙ − 1 2 -functions, we may show the upper and lower bounds of decay rates for the H ˙ − 1 2 weak solution of the surface quasi-strophic equation. Moreover, as a 1 2 -order derivative of H ˙ − 1 2 weak solution, we further derive an improved upper and lower bounds of decay rates for L 2 weak solution. The findings may be of independent interest and the technique can be also applied to the other related fluid dynamical model with solutions in the negative Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose the rectangle transformation problem (RTP) and its variants. RTP asks for rectangle partitions on two rectangles of the same area which produce two identical sets of pieces. We are interested in the minimum RTP which requires to minimize the partition size. This initiates the algorithmic study of dissection problems in module number optimization, particularly in the category of rectangle partition. We mainly focus on the strict rectangle transformation problem (SRTP) in which rotation is not allowed during the transformation. It has been shown that SRTP has no finite solution if the ratio of the two parallel side lengths of input rectangles is irrational. So we turn to its complemental case, SRTP with integral input, denoted by SIRTP, in which case both side lengths are assumed integral. We give a polynomial time algorithm ALGSIRTP which gives a solution at most q / p + 7 log 2 p to SIRTP (p , q) ( q ≥ p ), where p and q are two integral side lengths of input rectangles p × q and q × p . Note that q / p is an intrinsic lower bound for SIRTP (p , q) . So ALGSIRTP is a (7 log p) -approximation algorithm for minimum SIRTP (p , q) . On the other hand, we show that for any ε > 0 and any constant range (1 , 1 + δ) , there are integers p and q ( q > p ) of ratio q / p in this range, such that there is no solution less than max { q / p , log 2 1 - ε q } to SIRTP (p , q) . This is an almost tight bound since the algorithm ALGSIRTP gives an upper bound 7 log 2 p + O (1) in this case. We also raise a long series of open questions for further research along this line. [ABSTRACT FROM AUTHOR]

• Saint-Venant torsion of cylindrical orthotropic solid elliptical cross section. • Appropriate analytical solution for torsion and Prandtl stress functions. • Upper and lower bounds for the torsional rigidity. This paper deals with the Saint-Venant torsion of elastic cylindrical orthotropic solid elliptical cross section. The origin of the cylindrical anisotropy coincides with the centroid of the elliptical cross section. By the use of principle of minimum of potential energy and principle of minimum of complementary energy approximate analytical solutions are derived for the torsion function and for the Prandtl's stress function. Obtained upper and lower bounds for the torsional rigidity show the accuracy of the derived approximate analytic solutions. [ABSTRACT FROM AUTHOR]

• The spatially uncertain parameters are described by the interval field model with upper and lower bounds. • An interval iterative method is proposed for static response analysis of structures with spatial uncertainties which can effectively avoid the overestimation existing in traditional interval analysis. • The upper and lower bounds of the responses obtained by the proposed method could envelop the actual response bounds. Parameters with spatial uncertainties are very common in practical engineering, which could have a significant effect on structural performances. Different from the framework of probability theory, the interval field model describes the spatial uncertainty with upper and lower bounds rather than the probability distribution function or other statistical characteristics. By introducing the interval field model into finite element analysis and solving the resulting interval finite element equilibrium equation, the upper and lower bounds of structural responses can then be obtained. This paper proposes an interval iterative method for static displacement response analysis of structures with spatial uncertainties, effectively improving the overestimation existing in traditional interval analysis due to dependency problems and obtaining a compact interval envelope of the exact response bounds. Firstly, the spatially uncertain parameters described by the interval field are represented by the interval Karhunen–Loève (K-L) expansion, based on which the interval finite element equilibrium equation is formulated. Secondly, the interval finite element problem is decomposed into several subproblems, and an interval iterative method is developed for an envelope solution of the structural response bounds. Finally, the accuracy and efficiency of the proposed method are verified by several numerical examples. [ABSTRACT FROM AUTHOR]

There are several mathematical models that describe the propagation of cracks. For many engineering applications, up to a certain point, it is not necessary to have great accuracy in predictions about the behavior of the evolution of a crack, but a reliable prediction, within certain limits, of such behavior. This work presents theoretical results consisting in obtaining lower and upper bounds that "envelop" the first and second order statistical moment estimators of the crack size function based on the fast crack bounds method. These bounds are polynomials defined in the variable "number of cycles" that consider the uncertainties of the parameters that describe the crack propagation models. The performance of the bounds for the statistical moments of the crack size is evaluated through the relative deviation between the bounds and the approximate numerical solutions of the initial value problems (IVP) that describe the crack evolution laws. For this work, the Collipriest model is used. The Monte Carlo simulation method is used to create samples of the selected parameters to obtain the crack size for both the bounds and the Runge-Kutta method. [ABSTRACT FROM AUTHOR]

In this paper, we construct linear codes over Z 4 with bounded GC-content. The codes are obtained using a greedy algorithm over Z 4 . Further, upper and lower bounds are derived for the maximum size DNA codes of length n with constant GC-content w and edit distance d. [ABSTRACT FROM AUTHOR]

Group testing is the process of pooling arbitrary subsets from a set of $ {n}$ items so as to identify, with a minimal number of tests, a “small” subset of $ {d}$ defective items. In “classical” non-adaptive group testing, it is known that when $ {d}$ is substantially smaller than $ {n}$ , $\Theta ({d}\log ({n}))$ tests are both information-theoretically necessary and sufficient to guarantee recovery with high probability. Group testing schemes in the literature that meet this bound require most items to be tested $ {\Omega }(\log ({n}))$ times, and most tests to incorporate $ {\Omega }({{n/d}})$ items. Motivated by physical considerations, we study group testing models in which the testing procedure is constrained to be “sparse.” Specifically, we consider (separately) scenarios in which 1) items are finitely divisible and hence may participate in at most $ {\gamma } \in {o}(\log ({n}))$ tests; or 2) tests are size-constrained to pool no more than $\rho \in {o}({{n/d}})$ items per test. For both scenarios, we provide information-theoretic lower bounds on the number of tests required to guarantee high probability recovery. In particular, one of our main results shows that $ {\gamma }$ -finite divisibility of items forces any non-adaptive group testing algorithm with the probability of recovery error at most $ {\epsilon }$ to perform at least $ {\gamma } {d}({ {n/d}})^{({1}-{5} {\epsilon })/ {\gamma }}$ tests. Analogously, for $ {\rho }$ -sized constrained tests, we show an information-theoretic lower bound of $ {\Omega }({n}/ {\rho })$ tests for high-probability recovery–hence in both settings the number of tests required grows dramatically (relative to the classical setting) as a function of $ {n}$. In both scenarios, we provide both randomized constructions and explicit constructions of designs with computationally efficient reconstruction algorithms that require a number of tests that is optimal up to constant or small polynomial factors in some regimes of ${{n, d,}} {\gamma }$ , and $ {\rho }$. The randomized design/reconstruction algorithm in the $ {\rho }$ -sized test scenario is universal–independent of the value of $ {d}$ , as long as $ {\rho } \in {o}({\textbf {n/d}})$. We also investigate the effect of unreliability/noise in test outcomes, and show that whereas the impact of noise in test outcomes can be obviated with a small (constant factor) penalty in the number of tests in the $ {\rho }$ -sized tests scenario, there is no group-testing procedure, regardless of the number of tests, that can combat noise in the $ {\gamma }$ -divisible scenario. [ABSTRACT FROM AUTHOR]

Abstract A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. We study upper and lower bounds on the number of words in maximal finite towers between two regular languages with respect to the size of the NFA (respectively the DFA) representation. We show that the upper bound is polynomial in the number of states and exponential in the size of the alphabet, and that it is asymptotically tight if the size of the alphabet is fixed. If the alphabet may grow with the number of states of the automata, the lower bound on the height of towers is exponential with respect to that number. In this case the asymptotically optimal bound remains an open problem. Since, in many cases, the constructed towers are sequences of prefixes, we also study towers of prefixes. [ABSTRACT FROM AUTHOR]

Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as uncertain but bounded parameters, i.e. interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in a steady‐state current field with uncertain but bounded parameters efficiently. The uncertain parameters are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained from the equilibrium governing equation and by using the properties of interval mathematics, we calculate the upper and lower bounds of the electric potentials of a steady‐state current field. In order to evaluate the accuracy and efficiency of the proposed method, two numerical examples are used. The results illustrate that the precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of Monte Carlo simulation, which is the most widely used method related to uncertainties. Monte Carlo simulation requires a large number of samplings, and this leads to significant increase in runtime. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

This paper aims to develop an optimization approach for deriving the upper and lower bounds of transportation network vulnerability under simultaneous disruptions of multiple links without the need to evaluate all possible combinations as in the enumerative approach. Mathematically, we formulate the upper and lower bounds of network vulnerability as a binary integer bi-level program (BLP). The upper-level subprogram maximizes or minimizes the remaining network throughput under a given number of disrupted links, which corresponds to the upper and lower vulnerability bounds. The lower-level subprogram checks the connectivity of each origin-destination (O-D) pair under a network disruption scenario without path enumeration. Two alternative modeling approaches are provided for the lower-level subprogram: the virtual link capacity-based maximum flow problem formulation and the virtual link cost-based shortest path problem formulation. Computationally, the BLP model can be equivalently reformulated as a single-level mixed integer linear program by making use of the optimality conditions of the lower-level subprograms and linearization techniques for the complementarity conditions and bilinear terms. Numerical examples are also provided to systematically demonstrate the validity, capability, and flexibility of the proposed optimization model. The vulnerability envelope constructed by the upper and lower bounds is able to effectively consider all possible combinations without the need to perform a full network scan, thus avoiding the combinatorial complexity of enumerating multi-disruption scenarios. Using the vulnerability envelope as a network performance assessment tool, planners and managers can more cost-effectively plan for system protection against disruptions, and prioritize system improvements to minimize disruption risks with limited resources. [ABSTRACT FROM AUTHOR]

In highly dynamic wireless networks, communications face several challenges. In the first place, noise levels between nodes might be difficult to predict a priori. Besides, a Byzantine attacker hidden in the network, with knowledge of the network topology and observation of all transmissions, can choose arbitrary locations to inject corrupted packets. Considering that transmissions are usually in bits and hardware in wireless networks usually use modulation schemes with the size of modulation alphabet being powers of two, e.g. BPSK, QPSK, 16-QAM, 64-QAM, and so on, to address the above problem, we study coding for networks experiencing worst case bit errors, and with network codes over binary extension fields. We demonstrate that in this setup prior network error-correcting schemes can be arbitrarily far from achieving the optimal network throughput. A new transform metric for errors under the considered model is proposed. Using this metric, we replicate many of the classical results from coding theory. Specifically, new Hamming-type, Plotkin-type, and Elias-Bassalygo-type upper bounds on the network capacity are derived. A commensurate lower bound is shown based on Gilbert–Varshamov (GV)-type codes for error-correction. The GV codes used to attain the lower bound can be non-coherent, that is, they require neither prior knowledge of the network topology nor network coding kernels. We also propose a computationally efficient concatenation scheme. The rate achieved by our concatenated codes is characterized by a Zyablov-type lower bound. We provide a generalized minimum-distance decoding algorithm which decodes up to half the minimum distance of the concatenated codes. The end-to-end nature of our design enables our codes to be overlaid on the classical distributed random linear network codes. The other advantage of the end-to-end strategy over the link-by-link error-correction is that it reduces the computational cost at the internal nodes for performing error-correction. [ABSTRACT FROM PUBLISHER]

We consider a Riemannian cylinder Ω endowed with a closed potential 1-form A and study the magnetic Laplacian Δ A with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate. [ABSTRACT FROM AUTHOR]

It is known that the Borel-Cantelli Lemma plays an important role in probability theory. Many attempts were made to generalize its second part. In this article, we investigate the upper and lower bounds of Borel-Cantelli Lemma for the nonnegative functions in a general measure space. Our results extend the corresponding results obtained in a probability space. Some examples including dependent random variables are illustrated to our results. [ABSTRACT FROM AUTHOR]

In this paper, a modified Black–Scholes (B–S) model is proposed, based on a revised assumption that the range of the underlying price varies within a finite zone, rather than being allowed to vary in a semi-infinite zone as presented in the classical B–S theory. This is motivated by the fact that the underlying price of any option can never reach infinity in reality; a trader may use our new formula to adjust the option price that he/she is willing to long or short. To develop this modified option pricing formula, we assume that a trader has a view on the realistic price range of a particular asset and the log-returns follow a truncated normal distribution within this price range. After a closed-form pricing formula for European call options has been successfully derived, some numerical experiments are conducted. To further demonstrate the meaning of the proposed model, empirical studies are carried out to compare the pricing performance of our model and that of the B–S model with real market data. [ABSTRACT FROM AUTHOR]

We consider the problem of assigning radii to a given set of points in the plane, such that the resulting set of disks is connected, and the sum of radii is minimized. We prove that the problem is NP-hard in planar weighted graphs if there are upper bounds on the radii and sketch a similar proof for planar point sets. For the case when there are no upper bounds on the radii, the complexity is open; we give a polynomial-time approximation scheme. We also give constant-factor approximation guarantees for solutions with a bounded number of disks; these results are supported by lower bounds, which are shown to be tight in some of the cases. Finally, we show that the problem is polynomially solvable if a connectivity tree is given, and we conclude with some experimental results. [ABSTRACT FROM AUTHOR]

In this paper, one of our main purposes is to prove the boundedness of the solution set of tensor complementarity problems such that the specific bounds depend only on the structural properties of such a tensor. To achieve this purpose, firstly, we prove that this class of structured tensors is strictly semi-positive. Subsequently, the strictly lower and upper bounds of operator norms are given for two positively homogeneous operators. Finally, with the help of the above upper bounds, we show that the solution set of tensor complementarity problems has the strictly lower bound. Furthermore, the upper bounds of spectral radius are obtained, which depends only on the principal diagonal entries of tensors. [ABSTRACT FROM AUTHOR]

Bearing-supported shafts are widely used in various machines. Due to harsh working environments, bearing performance degrades over time. To prevent unexpected bearing failures and accidents, bearing performance degradation assessment becomes an emerging topic in recent years. Bearing performance degradation assessment aims to evaluate the current health condition of a bearing through a bearing health indicator. In the past years, many signal processing and data mining based methods were proposed to construct bearing health indicators. However, the upper and lower bounds of these bearing health indicators were not theoretically calculated and they strongly depended on historical bearing data including normal and failure data. Besides, most health indicators are dimensional, which connotes that these health indicators are prone to be affected by varying operating conditions, such as varying speeds and loads. In this paper, based on the principle of squared envelope analysis, we focus on theoretical investigation of bearing performance degradation assessment in the case of additive Gaussian noises, including distribution establishment of squared envelope, construction of a generalized dimensionless bearing health indicator, and mathematical calculation of the upper and lower bounds of the generalized dimensionless bearing health indicator. Then, analyses of simulated and real bearing run to failure data are used as two case studies to illustrate how the generalized dimensionless health indicator works and demonstrate its effectiveness in bearing performance degradation assessment. Results show that squared envelope follows a noncentral chi-square distribution and the upper and lower bounds of the generalized dimensionless health indicator can be mathematically established. Moreover, the generalized dimensionless health indicator is sensitive to an incipient bearing defect in the process of bearing performance degradation. [ABSTRACT FROM AUTHOR]

The paper considers the sigmoid function defined through the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided. [ABSTRACT FROM AUTHOR]

A fast general extension algorithm of Latin hypercube sampling (LHS) is proposed, which reduces the time consumption of basic general extension and preserves the most original sampling points. The extension algorithm starts with an original LHS of sizemand constructs a new LHS of sizem + nthat remains the original points. This algorithm is the further research of basic general extension, which cost too much time to get the new LHS. During selecting the original sampling points to preserve, time consumption is cut from three aspects. The first measure of the proposed algorithm is to select isolated vertices and divide the adjacent matrix into blocks. Secondly, the relationship of original LHS structure and new LHS structure is discussed. Thirdly, the upper and lower bounds help reduce the time consumption. The proposed algorithm is applied for two functions to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

In this article, a new method for estimating the volume of selected fruits and vegetables, using information obtained from three orthogonal images of the object is proposed. The method was based on a novel lower bound on this volume, combined with an application of a well-known upper bound. The lower bound was obtained by calculating the volume of an artificial object created from the intersection of the three object silhouettes. The method was applied to a significant range of food products and simple geometric objects, and it was found that the method estimated volume with approximately 11.9% error, generally, and 2%, for rounded objects, specifically. [ABSTRACT FROM AUTHOR]

Due to the difficulty in manipulating the distribution of Wishart random matrices, the performance analysis of multiple-input-multiple-output (MIMO) channels has mainly focused on deriving capacity bounds via Jensen’s inequality. However, to the best of our knowledge, the tightness of Jensen’s bounds has not yet been rigorously quantified in the general MIMO context. This paper proposes a new methodology for measuring the tightness of Jensen’s bounds via the sandwich theorem. In particular, we first compare the tightness of two different pairs of upper/lower bounds for a general class of MIMO channels based on the unordered eigenvalue of the instantaneous correlation matrix and for arbitrary numbers of antennas. The tightness of Jensen’s bounds in different channel scenarios is investigated including multiuser MIMO with maximal ratio combining. Our analysis is facilitated by deriving some new results for finite-dimensional Wishart matrices, i.e., for the arbitrary moments of the unordered eigenvalue of central and non-central Wishart matrices. Our results provide very interesting insights into the implications of the system parameters, such as the number of antennas, and signal-to-noise ratio, on the tightness of Jensen’s bounds, and showcase the suitability and limitations of Jensen’s bounds. [ABSTRACT FROM PUBLISHER]

In the graph of a complex network, the algebraic connectivity is the second smallest eigenvalue of a Laplacian matrix. In this paper, we present a cut algorithm based on edge centrality by minimizing the algebraic connectivity of graph. The edge centrality cut algorithm (ECCA) cuts edges at a time in order to reduce temporal complexity, the algebraic connectivity of which experiences the fastest decline. To prevent nodes from overcutting, each edge sets the weight. We use the advanced ECCA (AECCA) to detect overlapping communities by calculating the correlation coefficients of the nodes. This paper also proposes upper, lower and weaker lower bounds of algebraic connectivity. We demonstrate that our algorithms are effective and accurate at discovering community structure in both artificial and real-world network data and that the algebraic connectivity of the cut algorithm lies between the upper and lower bounds. Our algorithms offer new insights into community detection by calculating the edge centrality. [ABSTRACT FROM AUTHOR]

We study the impact of age-structure and temporal environmental variability on the persistence of populations. We use a linear age-structured model with time-dependent vital rates. It is the same as the one presented by Chipot in (Arch. Ration. Mech. Anal. 82(1):13-25, 1983), but the assumptions on the vital rates are slightly different. Our main interest is in describing the large-time behavior of a population provided that we know its initial distribution and transient vital rates. Using upper and lower solutions for the characteristic equation, we define time-dependent upper and lower boundaries for a solution in a constant environment. Moreover, we estimate solutions for the general time-dependent case and also for a special case when the environment is changing periodically. [ABSTRACT FROM AUTHOR]

In this paper we study the one-sided Hausdorff distance between the shifted Heaviside step--function and the transmuted Stannard growth function. Precise upper and lower bounds for the Hausdorff distance have been obtained. We present a software module (intellectual property) within the programming environment CAS Mathematica for the analysis of the growth curves. Numerical examples, illustrating our results are given, too. [ABSTRACT FROM AUTHOR]

We give explicit upper and lower bounds for a large subset of Comtet numbers s α (n , m) of the first kind, including the r -Stirling numbers of the first kind, among others. In many occasions, such estimates are asymptotically sharp. The form of the bounds varies according to m lying in the central or non-central regions of { 1 , ... , n }. Depending on this fact, we use different probabilistic representations of s α (n , m) in terms of well known random variables. [ABSTRACT FROM AUTHOR]

• The upper and lower response bounds are obtained through a series of sequential simulations. • The proposed sequential simulation method is applicable to interval uncertainty analysis of structural or system response with multiple DOFs. • The contributive samples for the response bounds over the whole concerned domain can be identified simultaneously. • The sequential simulation strategy is demonstrated to be more efficient than the direct MC simulation for response bounds evaluation. Prediction of response bounds of structures with interval uncertainties is a major concern in interval finite element analysis. In many cases, the structural response is a variable regarding to physical parameters such as location, node, time, or other degrees of freedom. Different kinds of interval methods have been proposed and developed for response bounds analysis, which mainly include the interval arithmetic-based methods, optimization methods, perturbation methods, etc. This paper proposes a sequential simulation strategy for response bounds analysis of structures with interval uncertainties, through which we aim to find the upper and lower bounds by implementing the simulation procedure sequentially. The proposed sequential simulation strategy suggests an initial sampling and simulation, from which those contributive samples that result in the current upper or lower response bound are retained. In the subsequent simulation sequence, local samples within neighborhoods of the present contributive samples as well as a set of global samples are generated for the input interval uncertainties. With such a simulation procedure, the response bounds are expected to expand outwards sequentially until convergence. By illustration and comparison, the proposed sequential simulation strategy is proved to be more efficient than the direct simulation method for structural response bounds analysis. [ABSTRACT FROM AUTHOR]

A family of three finite elements is developed for the lateral-torsional buckling analysis of thin-walled members with doubly symmetric cross-sections. The elements are based on a recently derived variational principle which incorporates shear deformation effects in conjunction with a special interpolation scheme ensuring C1 continuity. One of the elements is developed such that it consistently converges from above while another element is intended to consistently converge from below. The third element exhibits fast convergence characteristics compared to other elements but cannot be guaranteed to provide either an upper or a lower bound solution. The formulation incorporates the ability to enforce any set of linear multi-point kinematic constraints. The validity of the solution is established through comparisons with other well-established numerical solutions. The elements are then used to solve practical problems involving simply supported beams, cantilevers and continuous beams under a variety of loading conditions including concentrated loads, linear bending moments and uniformly distributed loads. The effect of lateral and torsional restraints and the location of lateral restraint along the section height on lateral-torsional buckling capacity of beams are also examined through examples. [ABSTRACT FROM AUTHOR]

In this note we prove more precise estimates for the approximation of the step function by sigmoidal logistic functions. Numerical examples, illustrating our results are given, too. [ABSTRACT FROM AUTHOR]

This paper studies the online maximum edge-weighted b -matching problem. The input of the problem is a weighted bipartite graph G = ( L , R , E , w ) . Vertices in R arrive online, and each vertex in L can be matched to at most b vertices in R . The objective is to maximize the total weight of the matching edges. We give a randomized algorithm Greedy-RT for this problem, and show that its competitive ratio is Ω ( 1 ∏ j = 1 log ⁎ ⁡ w max − 1 log ( j ) ⁡ w max ) where w max is an upper bound on the edge weights, which may not be known ahead of time. We can improve the competitive ratio to Ω ( 1 log ⁡ w max ) if w max is known to the algorithm when it starts. We also derive an upper bound O ( 1 log ⁡ w max ) on the competitive ratio, suggesting that Greedy-RT is near optimal. We also consider deterministic algorithms; we present a near optimal algorithm Greedy-D which has competitive ratio 1 1 + 2 ξ ( w max + 1 ) 1 ξ , where ξ = min ⁡ { b , ⌈ ln ⁡ ( 1 + w max ) ⌉ } . We also study a variant of the problem called online maximum two-sided vertex-weighted b -matching problem, and give a modification of the randomized algorithm Greedy-RT called Greedy- v RT for this variant. We show that the competitive ratio of Greedy- v RT is also near optimal. [ABSTRACT FROM AUTHOR]

In this paper, a comparative study of the simulated symbol error rate (SER) with the theoretical SER of uncoded communication systems is made for selected modulation schemes with and without fading. Slow fading Weibull and Rayleigh channels are considered in this paper. The modulation schemes considered are (1) Binary Phase Shift Keying, (2) Quadrature Phase Shift Keying, (3) Orthogonal Frequency Shift Keying and (4) M-ary Quadrature Amplitude Modulation. A novel series expansion for SER of selected modulation schemes in slow fading Weibull channels is considered. In addition, closed-form expressions for the upper and lower bounds of the SER for the aforementioned modulation schemes in the presence of AWGN and Weibull fading channels are derived and plotted. The simulated results are validated by comparing them with their theoretical results, upper and lower bounds. [ABSTRACT FROM AUTHOR]

In this article, we study adaptive stabilized mixed finite volume methods for the incompressible flows approximated using the lower order elements. A residual type of a posteriori error estimator is designed and studied with the derivation of upper and lower bounds between the exact solution and the finite volume solution. A discrete local lower bound between two successive finite volume solutions is also obtained. Also, convergence of the adaptive stabilized mixed finite volume methods is established. The presented methods have three prominent features. First, it is of practical convenience in real applications with the same partitions for velocity and pressure. Second, less computational time is required by easily applying both the lower order elements and the local grid refinement necessary for the elements of interest. Third, compared with the standard finite element method, its analysis of H1-norm and L2-norm for the velocity and pressure are usually derived without any high order regularity conditions on the exact solution. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1424-1443, 2015 [ABSTRACT FROM AUTHOR]

Abstract: In this paper we are interested in a rigorous analysis of the solution of a class of initial-value problems with singularities. We consider scalar non-autonomous IVPs with separated variables and one unknown singularity in each variable (which leads to four unknown ‘events’ in the two-dimensional space). Many algorithms proposed in the literature for singular IVPs are practically oriented. They do not avoid heuristic arguments, and are often checked for efficiency by numerical experiments. We design an adaptive algorithm with no heuristic steps for solving the considered problems, and provide rigorous bounds on the error. We show that in spite of the presence of singularities the algorithm preserves the (optimal) error known for the regular case. Lower bounds on the error of any algorithm in the case of a larger number of singularities are also discussed. [Copyright &y& Elsevier]

Abstract: The paper is devoted to a numerical Limit Analysis of a hollow spheroidal model with a Drucker–Prager solid matrix, for several values of the corresponding friction angle ϕ. In the first part of this study, the static and the mixed kinematic 3D-codes recently evaluated in [1] are modified to use the geometry defined in [2] for spheroidal cavities in the context of a von Mises matrix. The results in terms of macroscopic criteria are satisfactory for low and medium values of ϕ, but not enough for in the highly compressive part of the criterion. To improve these results, an original mixed approach, dedicated to the axisymmetric case, was elaborated with a specific discontinuous quadratic velocity field associated with the triangular finite element. Despite the less good conditioning inherent to the axisymmetric modelization, the resulting conic programming problem appears quite efficient, allowing one take into account numerical discretization refinements unreachable with the corresponding 3D mixed code. After a first validation in the case of spherical cavities whose exact solution is known, the final results for spheroidal voids are given for three usual values of the friction angle and two values of the cavity aspect factor. [Copyright &y& Elsevier]

Abstract: We study the solution of piecewise regular systems of IVPs with a switching hypersurface defined by an unknown event function. Our aim is to design an algorithm that is not based on heuristic steps, it does not use information on the event function and preserves the order known for regular systems. The algorithm is based on the adaptive mesh which differs from the equidistant mesh only by a single point. We provide a rigorous (that is, independent of heuristic arguments) analysis of its error and cost. [Copyright &y& Elsevier]