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The Posit Number System was introduced in 2017 as a replacement for floating-point numbers. Since then, the community has explored its application in Neural Network related tasks and produced some unit designs which are still far from being competitive with their floating-point counterparts. This paper proposes a Posit Logarithm-Approximate Multiplication (PLAM) scheme to significantly reduce the complexity of posit multipliers, the most power-hungry units within Deep Neural Network architectures. When comparing with state-of-the-art posit multipliers, experiments show that the proposed technique reduces the area, power, and delay of hardware multipliers up to 72.86%, 81.79%, and 17.01%, respectively, without accuracy degradation.

The aggregate signature is a special signature mode widely used in the wireless medical sensor network. The aggregate signature can reduce bandwidth and storage space in this sensor network by aggregating multiple signatures from different signers into a short signature. Traditional aggregate signature protocols based on the discrete logarithm problem and the great integer factorization problem cannot resist quantum attacks. In this article, we propose a new noninteractive identity-based aggregate signature protocol from lattices. We prove that the proposed protocol is secure in the quantum random oracle model. Additionally, the performance of the proposed protocol is much better than most previous protocols according to our experiment. Meanwhile, the size of the aggregate signature in our protocol is a logarithmic function of the number of signatures being aggregated.

The main limitation of Smoothed Particle Hydrodynamics (SPH) method that resists the method's potential is its lack of providing stability and accuracy to the numerical technique. We improve the accuracy of the standard SPH technique, by formulating a new inverse logarithmic kernel function. This new kernel function is derived based on the underlying properties of kernel functions. The approximation technique used here is based on the Moving Least Squares based technique. The adequacy of the proposed kernel function is tested by simulation of 2D shock wave propagation and 3D dam-break free surface flow against a cuboidal obstacle. The method was validated against experimental data by Kleefsman et al., [1] . The numerical results reveal that our new SPH approach using inverse logarithmic kernel function outperforms existing ones in particle restoration, zero error, better accuracy and enhanced efficiency in kernel approximation. This new kernel function showed some improvement over existing kernels by showing very less error approximation value of 0.035h2. The results showed some improvements over standard technique by being capable of handling problems with large deformations accurately and precisely.

Since the development of higher local class field theory, several explicit reciprocity laws have been constructed. In particular, there are formulas describing the higher-dimensional Hilbert symbol given, among others, by M. Kurihara, A. Zinoviev and S. Vostokov. K. Kato also has explicit formulas for the higher-dimensional Kummer pairing associated to certain (one-dimensional) $p$-divisible groups. In this paper we construct an explicit reciprocity law describing the Kummer pairing associated to any (one-dimensional) formal group. The formulas are a generalization to higher-dimensional local fields of Kolyvagin's reciprocity laws. The formulas obtained describe the values of the pairing in terms of multidimensional $p$-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups. In the second part of this paper, we will apply the results obtained here to give explicit formulas for the generalized Hilbert symbol and the Kummer pairing associated to a Lubin-Tate formal group. The results obtained in the second paper constitute a generalization to higher local fields, of the formulas of Artin-Hasse, K. Iwasawa and A. Wiles., The stronger reciprocity laws in this new version cover arbitrary higher local fields, as opposed to only standard higher local fields

A learning-based online optimal sliding-mode control strategy is developed for space circumnavigation missions subject to input constraints, and the mismatched uncertainties caused by measurement uncertainties are also considered in this infinite-horizon optimal control problem. The logarithmic hyperbolic cosine function is used to design the optimal value function to overcome the weakness that the derivative of the adaptive weight of neural network (NN) changes too fast when the value of the sliding-mode function is too large, and another suitable nonquadratic function is used to incorporate input constraints into the optimal control framework. To approximate the Hamiton-Jacobi-Bellman equation corresponding to the novel optimal value function, an actor-critic (AC) architecture is introduced with NNs, and a finite-time disturbance observer (FTDO) is employed to estimate the mismatched uncertainties in the plant. The simulation results verify the effectiveness of the proposed approach.

Static black hole with the Power Maxwell invariant (PMI), Born–Infeld (BI), logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional spacetime with cosmological constant was studied. It was shown that the LN and EN fields represent the Born–Infeld type of nonlinear electrodynamics. It the framework of General Relativity the exact solutions of the field equations were obtained, corresponding thermodynamic functions were calculated and the [Formula: see text] criticality of the black holes in the extended phase-space thermodynamics was investigated.

Let B n ( m ) be a set picked uniformly at random among all m-elements subsets of { 1 , 2 , … , n } . We provide a pathwise construction of the collection ( B n ( m ) ) 1 ⩽ m ⩽ n and prove that the logarithm of the least common multiple of the integers in ( B n ( ⌊ m t ⌋ ) ) t ⩾ 0 , properly centered and normalized, converges to a Brownian motion when both m , n tend to infinity. Our approach consists of two steps. First, we show that the aforementioned result is a consequence of a multidimensional central limit theorem for the logarithm of the least common multiple of m independent random variables having uniform distribution on { 1 , 2 , … , n } . Second, we offer a novel approximation of the least common multiple of a random sample by the product of the elements of the sample with neglected multiplicities in their prime decompositions.

This article suggests a new hypergeometric function for function fields and a new operator such that the Drinfeld logarithm is stable under it, and studies an equation satisfied by the hypergeometric function. As applications, our function is related to a supersingular polynomial of Drinfeld modules, a period of Drinfeld modules, and the Kochubei's polylogarithm, which are function-field analogues of well-known facts for the classical setting. Moreover, we generalize results for the Carlitz modules proven by Thakur to those for the Drinfeld ones.

Diffusion affine projection algorithms have the ability to de-correlate the input signal and have faster convergence but with the expense of increased computational complexity. Moreover, traditional diffusion affine projection algorithms consider the noise to be of Gaussian nature. However, practically this noise can be non-Gaussian which can significantly deteriorate the convergence of the algorithms. To mitigate this issue in this brief, we propose two robust affine projection algorithms based on the generalized maximum correntropy criterion (d-A-GMCC) and the logarithmic hyperbolic cosine cost function (d-A-lncosh). To reduce the computational expense of the proposed algorithms, we propose dichotomous coordinate descent based d-A-GMCC and d-A-lncosh algorithms. Extensive simulation study for different Gaussian and non-Gaussian noise environments shows the improved estimation ability of proposed algorithms.

The consensus control of second-order linear multi-agent systems with velocity constraint under directed graphs is investigated. In this brief, a new distributed sliding mode control scheme is proposed. The novelty of this scheme is that we integrate the logarithmic barrier function with the sliding surface, then the consensus is achieved by showing the convergence of the sliding variable to zero, meanwhile, the boundedness of the sliding variable indicates the velocity constraint is satisfied. With the proposed method, the semi-global consensus control of second-order linear multi-agent systems with velocity constraints can be easily achieved under directed graph. The effectiveness of the results is illustrated through a numerical example.

The engine knock simulator is useful for the evaluation of the feedback knock controllers and also the calibration of the feedforward control input without experiments in spark-ignition engines. This paper proposes a Mixture Density Network(MDN)-based statistical simulator of the engine knock for spark-ignition engines. The simulator can output the simulated knock intensity by the operating condition, which has a consistent probability distribution with the real engine. The statistical analysis is conducted based on the experimental data. According to the analysis results, several important properties about the knock intensity have been revealed. The logarithm of knock intensity is independent and identically distributed under an identical operating condition, whose probability distribution can be approximated by Gaussian Mixture Model(GMM). The parameter vector of the GMM is a function of the engine's operation condition. Based on these statistical properties of engine knock, we formulate the problem of establishing a statistical simulator, which includes two sub-problems. The first one is how to approximate the function from the operating condition to the parameters of the GMM. The second one is how to output the simulated random data of logarithm of knock intensity that obeys a given distribution. The MDN and the accept-reject algorithm are applied to solve the two sub-problem, respectively. Finally, we conducted experimental data-based validations to verify the proposed method.

The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence. There have been several works about BIHT but a theoretical understanding of the corresponding approximation error and convergence rate still remains open. This paper shows that the normalized version of BIHT (NBHIT) achieves an approximation error rate optimal up to logarithmic factors. More precisely, using $m$ one-bit measurements of an $s$-sparse vector $x$, we prove that the approximation error of NBIHT is of order $O \left(1 \over m \right)$ up to logarithmic factors, which matches the information-theoretic lower bound $\Omega \left(1 \over m \right)$ proved by Jacques, Laska, Boufounos, and Baraniuk in 2013. To our knowledge, this is the first theoretical analysis of a BIHT-type algorithm that explains the optimal rate of error decay empirically observed in the literature. This also makes NBIHT the first provable computationally-efficient one-bit compressed sensing algorithm that breaks the inverse square root error decay rate $O \left(1 \over m^{1/2} \right)$., Comment: Submitted to a journal

The fully parabolic cross-diffusion system { e u t = Δ u − χ ∇ ⋅ ( u v ∇ v ) , v t = Δ v − v + u , is considered under homogneous Neumann boundary conditions in a ball Ω ⊂ R n , n ≥ 1 , for e ∈ ( 0 , 1 ) and χ > 0 . Previous literature has asserted global existence of certain generalized solutions whenever χ n ( n − 2 ) + , but no result on any unboundedness phenomenon seems available; only in a parabolic-elliptic simplification, some solutions are known to blow up in finite time when n ≥ 3 and χ > 2 n n − 2 . The present study examines the solution behavior in the singular limit e ↘ 0 , and based on an essentially well-known result on finite-time blow-up in an accordingly obtained nonlocal scalar parabolic problem, under the assumptions that n ≥ 3 and χ > n n − 2 a statement on spontaneous emergence of arbitrarily large values of u for appropriately small e is derived.

In this paper, a damped p-Laplacian type wave equation with logarithmic nonlinearity is considered and finite time blow-up of solutions is proved with initial data at different initial energy levels. More precisely, when the initial energy is subcritical, a sufficient condition for the solutions to blow up in finite time is derived, by combining the Nehari manifold with concavity argument. When the initial energy is supercritical, some new skills are invented to establish another finite time blow-up criterion for this problem. Meanwhile, for each of the above two cases, the lifespan of the weak solutions is estimated from above. Moreover, by making full use of the strongly damping term and choosing appropriate parameters, a lower bound for the blow-up time is given.

Dynamic wavelet amplitude spectra extraction (DWASE), which is an ill-posed problem, is of great importance for nonstationary seismic data processing. The most difficult challenge is how to decouple the dynamic wavelets and reflection coefficients. The traditional DWASE methods solve the ill-posed problem depending on some prior information, such as the piecewise stationary hypothesis or estimation of the attenuation factor Q. In this article, we propose a multitask learning-based DWASE method and apply the method for Q estimation. Our proposed method can reduce the multiplicity of the ill-posed problem by estimating the logarithmic time-frequency amplitude spectrum (logarithmic TFAS) of both reflection coefficients and dynamic seismic wavelets, simultaneously. In our method, a parameter-sharing U-net is used to extract the logarithmic TFAS of the reflection coefficients and dynamic wavelets from the logarithmic TFAS of the nonstationary seismic data. To verify the accuracy of the DWASE results of our method, we make a quantitative analysis of the synthetic seismic data, which are obtained by our method and some traditional methods. We also apply the DWASE results of our method for Q estimation and attenuation compensation in both synthetic and field seismic data, to prove the effectiveness of the method. Also, comparisons with some traditional methods are given.

In this letter, different polarization characteristics of the sea clutter and target are considered to address the sea-surface weak target detection problem. We first construct a logarithmic generalized likelihood ratio test (log-GLRT) problem under the compound Gaussian model by considering multiple texture factors of sea clutter and four polarized channels. Based on the log-GLRT framework, a multivariable optimization problem is formulated to obtain the characteristic parameters of sea clutter and target. Then, under the block majorization-minimization (block-MM) framework, three parameters' estimation strategies are designed to solve the optimization problem of the proposed parameters. Finally, a log-GLRT-based polarimetric detector is proposed by applying the estimated characteristic parameters. The experimental results on the Intelligent PIxel processing Xband (IPIX) data sets demonstrate that our proposed detector can achieve better detection performance than the several existed detectors.

We consider the regression problem of estimating functions on $ \mathbb{R}^D $ but supported on a $ d $-dimensional manifold $ \mathcal{M} ~~\subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear approximation, we construct low-dimensional coordinates on $ \mathcal{M} $ at multiple scales, and perform multiscale regression by local polynomial fitting. We propose a data-driven wavelet thresholding scheme that automatically adapts to the unknown regularity of the function, allowing for efficient estimation of functions exhibiting nonuniform regularity at different locations and scales. We analyze the generalization error of our method by proving finite sample bounds in high probability on rich classes of priors. Our estimator attains optimal learning rates (up to logarithmic factors) as if the function was defined on a known Euclidean domain of dimension $ d $, instead of an unknown manifold embedded in $ \mathbb{R}^D $. The implemented algorithm has quasilinear complexity in the sample size, with constants linear in $ D $ and exponential in $ d $. Our work therefore establishes a new framework for regression on low-dimensional sets embedded in high dimensions, with fast implementation and strong theoretical guarantees.

This letter proposes a novel method based on multiscale dual morphological reconstruction (MDMR) to detect low-contrast ship target with unknown size and polarity (bright or dark) in infrared image. First, the multiscale morphological reconstruction perceives the structural information of various scales. The target signal map (TSM) is presented to indicate the target polarity and enhance target by background subtraction and logarithmic histogram transform. Next, the boundary constraint entropy threshold selection (BCETS) is designed to extract candidate targets and avoid the over- or under-segmentation problems. Then, the local contour contrast descriptor (LCCD) is constructed and the discriminant rule of low-contrast target is established to identify true target and eliminate false alarms. Finally, the pixel-or operation fuses the multiscale detection results. Extensive experiments show that the proposed method has a better effectiveness and robustness against compared methods.

Objective functions are critical for successful seismic fullwaveform inversions (FWIs). Deconvolution-based objective functions yielded promising results in time- and frequency-domain inversions. In this study, we developed two deconvolution-based objective functions for Laplace-domain inversions. These objective functions are based on convolutional filters that transform one of the observed or modeled data into another. The objective functions are derived by forcing the convolutional filter to be a zero-lag delta function by updating the model parameters. We could obtain a relatively simple objective function in the Laplace domain since the convolution in the time domain is equivalent to the multiplication function in the Laplace domain and the Laplace transform of the delta function is unity. We compared the new deconvolution-based objective functions and the conventional logarithmic objective function using synthetic and Gulf of Mexico field data and obtained similar inversion results. We showed that the logarithmic objective function conventionally used in Laplace-domain FWIs can be understood in the framework of deconvolution-based objective functions, which explains the similar inversion results.

We consider asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case. In the degenerate drift-diffusion equation, it is known that large time behavior of solutions converges to the Zel'dovich–Kompaneetz–Barenblatt (ZKB) function. For a fast-diffusion case, we show that the asymptotic profile for a solution is the generalized ZKB function such as the Talenti function. We use the entropy dissipation method combining the logarithmic Sobolev and the Shannon inequalities for the Renyi entropy that is known as an extension of the Boltzmann–Shannon entropy.

We revisit the maximal clique enumeration algorithm cliques by Tomita et al. that appeared in Theoretical Computer Science in 2006. It is known to work in O ( 3 n / 3 ) -time in the worst-case for an n-vertex graph. This is worst-case optimal with respect to the input size, but there is little knowledge about its performance with respect to the output. In this paper, we extend the time-complexity analysis with respect to the maximum size and the number of maximal cliques, and to its delay, solving issues that were left as open problems since the original paper. In particular, we prove that cliques has Ω ( 3 n / 6 ) delay and that, even if we allow to change the pivoting strategy, a variant having polynomial delay cannot be designed unless P = N P . These same results apply to the related Bron-Kerbosch algorithm. On the positive side, we show that the complexity of cliques and Bron-Kerbosch is amortized polynomial on graphs with logarithmic clique number. As these algorithms are widely used and regarded as fast “in practice”, we are interested in observing their practical behavior: we run an evaluation of cliques and three Bron-Kerbosch variants on over 130 real-world and synthetic graphs, observing how the clique number almost always satisfies our logarithmic constraint, and that their performance seems far from its theoretical worst-case behavior in terms of both total time and delay. 1

Since first introduced by Sudakov and Vu in 2008, the study of resilience problems in random graphs received a lot of attention in probabilistic combinatorics. Of particular interest are resilience problems of spanning structures. It is known that for spanning structures which contain many triangles, local resilience cannot prevent an adversary from destroying all copies of the structure by removing a negligible amount of edges incident to every vertex. In this paper we generalise the notion of local resilience to $H$-resilience and demonstrate its usefulness on the containment problem of the square of a Hamilton cycle. In particular, we show that there exists a constant $C > 0$ such that if $p \geq C\log^3 n/\sqrt{n}$ then w.h.p. in every subgraph $G$ of a random graph $G_{n, p}$ there exists the square of a Hamilton cycle, provided that every vertex of $G$ remains on at least a $(4/9 + o(1))$-fraction of its triangles from $G_{n, p}$. The constant $4/9$ is optimal and the value of $p$ slightly improves on the best-known appearance threshold of such a structure and is optimal up to the logarithmic factor., 40 pages, 7 figures; published version

We study a geometric property related to spherical hyperplane tessellations in R d . We first consider a fixed x on the Euclidean sphere and tessellations with M ≫ d hyperplanes passing through the origin having normal vectors distributed according to a Gaussian distribution. We show that with high probability there exists a subset of the hyperplanes whose cardinality is on the order of d log ⁡ ( d ) log ⁡ ( M ) such that the radius of the cell containing x induced by these hyperplanes is bounded above by, up to constants, d log ⁡ ( d ) log ⁡ ( M ) / M . We extend this result to hold for all cells in the tessellation with high probability. Up to logarithmic terms, this upper bound matches the previously established lower bound of Goyal et al. (1998) [6] .

The purpose of this paper is to establish restrictions on the parameters under which a function in the form of a natural logarithm of a linear fractional function is a decreasing generator. In addition to the general case, all special cases of generators of this type are considered. A triangular norm is constructed for each generator. In fact, a new parametric class of decreasing generators that generalizes and systematizes known generators is proposed. Such generators generate triangular norms represented by rational functions. The results of this paper can be used to construct aggregation operations.

International audience; Graphene Nanoribbons (GN), being an important class of next-generation carbon materials, are of immense interest and find innumerable applications in diverse fields. A variation of the generalized Lambert W function, called the Offset Logarithm function, has been found to have important applications in fields such as physics, engineering and nanotechnology. We study the electronic properties of zigzag GN and use the generalized Lambert W function to study the eigenvalue equations of the massless Dirac equation applied to zigzag GN. We have studied the effects of nanoribbon width and determined the parameters that significantly affect the obtained solutions.

We consider a 2 × 2 system of hyperbolic-parabolic balance laws. Our system is the converted form under inverse Hopf-Cole transformation of a Keller-Segel type chemotaxis model with logistic growth, logarithmic sensitivity, non-diffusive chemical signal and density-dependent production/consumption rate. We study Cauchy problem when the Cauchy data are near a diffusive contact wave. The contact wave connects two different end-states as x → ± ∞ , reflecting the situation when the logarithmic singularity plays an intrinsic role in the original chemotaxis model. We establish global existence of solution and study time asymptotic behavior of the solution. Consequently, we obtain nonlinear stability of the diffusive contact wave. Our result shows a significant difference when comparing our model to Euler equations with damping. In our case, there exists a secondary wave in the asymptotic ansatz. Therefore, the solution to Cauchy problem converges to the diffusive contact wave slower than in the case of Euler equations with damping. Besides its own physical relevance, our model is a prototype of a general system of hyperbolic-parabolic balance laws. Our results shed light on the future study of nonlinear stability of elementary waves for a general system.

In this paper, we propose a lightweight privacy-preserving Faster R-CNN framework (SecRCNN) for object detection in medical images. Faster R-CNN is one of the most outstanding deep learning models for object detection. Using SecRCNN, healthcare centers can efficiently complete privacy-preserving computations of Faster R-CNN via the additive secret sharing technique and edge computing. To implement SecRCNN, we design a series of interactive protocols to perform the three stages of Faster R-CNN, namely feature map extraction, region proposal and regression and classification. To improve the efficiency of SecRCNN, we improve the existing secure computation sub-protocols involved in SecRCNN, including division, exponentiation and logarithm. The newly proposed sub-protocols can dramatically reduce the number of messages exchanged during the iterative approximation process based on the coordinate rotation digital computer algorithm. Moreover, the effectiveness, efficiency and security of SecRCNN are demonstrated through comprehensive theoretical analysis and extensive experiments. The experimental findings show that the communication overhead in computing division, logarithm and exponentiation decreases to 36.19%, 73.82% and 43.37%, respectively.

Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a likelihood ratio between two models as a measure for indicating change. The first model is a single bernoulli variable while the second model divides the stored data in two segments, and models each segment with its own bernoulli variable. Finding the optimal split can be done in \( \mathcal {O} \mathopen {}\left( n\right) \) time, where n is the number of entries since the last change point. This is too expensive for large n. To combat this we propose an approximation scheme that yields \((1 - \epsilon )\) approximation in \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log ^2 n\right) \) time. The speed-up consists of several steps: First we reduce the number of possible candidates by adopting a known result from segmentation problems. We then show that for fixed bernoulli parameters we can find the optimal change point in logarithmic time. Finally, we show how to construct a candidate list of size \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log n\right) \) for model parameters. We demonstrate empirically the approximation quality and the running time of our algorithm, showing that we can gain a significant speed-up with a minimal average loss in optimality.

Let $\mathcal{A}$ denote the class of analytic functions in the open unit disc $\mathbb{U}$ normalized by $f(0)=f^{\prime }(0)-1=0,$ and let $\mathcal{S}$ be the class of all functions $f\in\mathcal{A}$ which are univalent in $\mathbb{U}$. For a function $f\in \mathcal{S}$, the logarithmic coefficients $\delta _{n}\,\left( n=1,2,3,\ldots \right) $ are defined by$\log \frac{f(z)}{z}=2\sum_{n=1}^{\infty }\delta _{n}z^{n}\qquad \left( z\in\mathbb{U}\right).$and it is known that $\left\vert \delta _{1}\right\vert \leq 1$ and $\left\vert \delta _{2}\right\vert \leq \frac{1}{2}\left( 1+2e^{-2}\right)=0,635\cdots .$ The problem of the best upper bounds for $\left\vert \delta_{n}\right\vert $ of univalent functions for $n\geq 3$ is still open. Let $\mathcal{SL}^{k}$ denote the class of functions $f\in \mathcal{A}$ such that$\frac{zf^{\prime }\left( z\right) }{f(z)}\prec \frac{1+\tau _{k}^{2}z^{2}}{1-k\tau _{k}z-\tau _{k}^{2}z^{2}},\quad \tau _{k}=\frac{k-\sqrt{k^{2}+4}}{2}\qquad \left( z\in \mathbb{U}\right).$In the present paper, we determine the sharp upper bound for $\left\vert\delta _{1}\right\vert ,\left\vert \delta _{2}\right\vert $ and $\left\vert\delta _{3}\right\vert $ for functions $f$ belong to the class $\mathcal{SL}^{k}$ which is a subclass of $\mathcal{S}$. Furthermore, a general formula is given for $\left\vert \delta _{n}\right\vert \,\left( n\in \mathbb{N}\right) $ as a conjecture.

T-Spherical fuzzy set (TSFS) is an improved extension in fuzzy set (FS) theory that takes into account four angles of the human judgment under uncertainty about a phenomenon that is membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). The purpose of this manuscript is to introduce and investigate logarithmic aggregation operators (LAOs) in the layout of TSFSs after observing the shortcomings of the previously existing AOs. First, we introduce the notions of logarithmic operations for T-spherical fuzzy numbers (TSFNs) and investigate some of their characteristics. The study is extended to develop T-spherical fuzzy (TSF) logarithmic AOs using the TSF logarithmic operations. The main theory includes the logarithmic TSF weighted averaging (LTSFWA) operator, and logarithmic TSF weighted geometric (LTSFWG) operator along with the conception of ordered weighted and hybrid AOs. An investigation about the validity of the logarithmic TSF AOs is established by using the induction method and examples are solved to examine the practicality of newly developed operators. Additionally, an algorithm for solving the problem of best production choice is developed using TSF information and logarithmic TSF AOs. An illustrative example is solved based on the proposed algorithm where the impact of the associated parameters is examined. We also did a comparative analysis to examine the advantages of the logarithmic TSF AOs.

In the paper is presented Neuro-Fuzzy System as a decision-making support in the selection of construction machines (the example of selecting a loader is provided). Construction characteristics of a loader make the basis for selection, but also other elements of importance. The data for Neuro-Fuzzy System modeling are prepared using the Multi-Criteria Decision Making (MCDM) methods: Logarithm Methodology of Additive Weights (LMAW), VIKOR, TOPSIS, MOORA and SAW. The paper also presents the method of aggregation of weights of rules premises (AWRP), which defines the key rules of Neuro-Fuzzy System. Finally, the training of the model is tested. The data for the selection of input variables and for model training are obtained by engaging experts.

In ths paper, we consider a new stability results of solutions to class of wave equations with weak, strong damping terms and logarithmic source in $\mathbb{R}^n$. We prove general stability estimates by introducing suitable Lyapunov functional.

In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.

We evaluate definite integrals of the form given by $\int_{0}^{\infty}R(a, x)\log (\cos (\alpha) \text{sech}(x)+1)dx$. The function $R(a, x)$ is a rational function with general complex number parameters. Definite integrals of this form yield closed forms for famous integrals in the books of Bierens de Haan [4] and Gradshteyn and Ryzhik [5].

In this paper we present two deterministic distributed algorithms for the Steiner tree (ST) problem in the CONGEST model. The first algorithm computes a 2 ( 1 − 1 / l ) -approximate ST using O ( S + n log ⁎ ⁡ n ) rounds and O ( m S + n 3 / 2 ) messages for a graph of n nodes and m edges, where S is the shortest path diameter of the graph and l is the number of leaf nodes in the optimal ST. It improves the round complexity of the best distributed ST algorithm known so far, which is O ˜ ( S + min { S t , n } ) [34] , where t is the number of terminal nodes. The second algorithm improves the message complexity of the first one by dropping the additive term of O ( n 3 / 2 ) at the expense of a logarithmic multiplicative factor in the round complexity. We also show that for graphs with S = O ( log ⁡ n ) , a 2 ( 1 − 1 / l ) -approximate ST can be deterministically computed using O ˜ ( n ) rounds and O ˜ ( m ) messages and these complexities almost coincide with the results of some of the singularly-optimal minimum spanning tree (MST) algorithms proposed in [15] , [22] , [37] .

The production of true color images requires observational data in the red, green, and blue (RGB) bands. The Advanced Geostationary Radiation Imager (AGRI) onboard China’s Fengyun-4 (FY-4) series of geostationary satellites only has blue and red bands, and we therefore have to synthesize a green band to produce RGB true color images. We used random forest regression and conditional generative adversarial networks to train the green band model using Himawari-8 Advanced Himawari Imager data. The model was then used to simulate the green channel reflectance of the FY-4 AGRI. A single-scattering radiative transfer model was used to eliminate the contribution of Rayleigh scattering from the atmosphere and a logarithmic enhancement was applied to process the true color image. The conditional generative adversarial network model was better than random forest regression for the green band model in terms of statistical significance (e.g., a higher determination coefficient, peak signal-to-noise ratio, and structural similarity index). The sharpness of the images was significantly improved after applying a correction for Rayleigh scattering, and the images were able to show natural phenomena more vividly. The AGRI true color images could be used to monitor dust storms, forest fires, typhoons, volcanic eruptions, and other natural events.