Exponential Space Research Articles

Attributes of Activation Energy and Exponential Based Heat Source in Flow of Carreau Fluid with Cross-Diffusion Effects

Abstract In the present study we aim to model and examine the impact of melting and double stratification on MHD flow of Carreau liquid over a stretching sheet. Incompressible non-Newtonian liquid is electrically conducting and exposed to a constant magnetic field. The exponential space dependent internal heat source effect is incorporated in the energy expression. Mass transfer is characterized in terms of activation energy and a binary chemical reaction. In addition, Soret and Dufour phenomena are included. The boundary layer concept is utilized to simplify the governing equations. A system of ordinary differential equations is obtained through proper transformations. The coupled non-linear system is then computed by the NDSolve technique. Plots and tabulated values are arranged for interpretation of different variables. The obtained results show that the flow field is influenced appreciably by melting, the heat source, the reaction rate and the activation energy. Moreover, Nusselt and Sherwood numbers are increased by the activation energy.

On a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents

ABSTRACTIn this paper, we are concerned with questions of the existence of solution for a class of nonlocal and nonhomogeneous Neumann boundary value problems involving the -Laplacian in which the nonlinear terms assume both critical growth. The main tools used are the Lions' Concentration-Compactness Principle [Lions PL. The concentration-compactness principle in the calculus of variations. The limit case I, part 1. Rev Mat Iberoam. 1985;1(1):145–201.] for variable exponent spaces and the Mountain Pass Theorem.

Multi-robot adversarial patrolling: Handling sequential attacks

Robot teams are commonly used for security tasks, where they are required to repeatedly monitor an area in order to prevent penetrations, initiated by an adversary. Current research in this field focuses mainly on detecting penetration attempts, but not on responding. Requiring the robots to also inspect and handle the penetrations has a significant impact on the patrol, as each penetration attempt also influences the robots' behavior, making them vulnerable to multiple attacks. Moreover, a knowledgeable adversary can initiate two sequential attacks, where the second attempt exploits the vulnerable points caused by the requirement that a robot handle the first penetration attempt. In this work, we consider the problem of sequential attacks and examine different robot policies against such adversarial behavior. We provide an optimal patrol strategy for various penetration attempt patterns. Our novel approach considers a full history-length policy, while previous work only handled very limited lengths of history. The use of a longer history improves the results. Moreover, we show how to significantly reduce, in practice, the exponential space state of the problem, while maintaining the optimality of the solution.

BMO–VMO results for fractional integrals in variable exponent Morrey spaces

We prove the boundedness of the fractional integration operator of variable order α(x) in the limiting Sobolev case α(x)p(x)=n−λ(x) from variable exponent Morrey spaces Lp⋅,λ⋅Ω into BMO (Ω), where Ω is a bounded open set. In the case α(x)≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces VLp⋅,λ⋅Ω into VMO (Ω). The results seem to be new even when p and λ are constant.

A Polynomial-Time Algorithm to Obtain State Machine Cover of Live and Safe Petri Nets

A method to find the minimized state machine cover of live and safe Petri nets (PNs) is proposed in this paper. It is required that a cover be obtained in some implementation methods of PN-based control algorithms and other applications such as data mining. Most of the known methods of its computation have at least exponential time and space complexity; this is true not only for the methods which guarantee a minimal cover is obtained but also for some methods of finding approximate solutions. The proposed algorithm is an approximation algorithm and has polynomial computational complexity. The experimental verification shows a very high efficiency of the presented technique. The proposed method is especially valuable in the case of large systems where a solution is obtained hundreds of times quicker than by other methods.

Equivalence among variable exponent Hardy or Bergman spaces

We study the question of when two weighted variable exponent Bergman spaces or Hardy spaces are equivalent. As an application, we show that variable exponent Hardy spaces have a close relation to classical Hardy spaces when the exponent is log-Hölder continuous and has bounded harmonic conjugate (when extended from its boundary values to be harmonic in the disc). We use this to characterize Carleson measures for these variable exponent Hardy spaces. We also prove under certain conditions an analogue of Littlewood subordination and a result on the boundedness of composition operators.

Reinventing known results in FCA: Notes on two recently published algorithms for computation of formal concepts

Two recently published algorithms for computation of formal concepts are analyzed. The first algorithm, by Ma et al. (2016), is claimed to provide a new and efficient algorithm for generating all object-oriented concepts. We recall that the generating of all object-oriented concepts and generating of all standard concepts is basically the same problem, since the object-oriented case and the standard case are easily reducible to each other via the set complement. Taking this reducibility into account, Ma et al. merely repeat results by Qian and Wei (2014). The algorithm is not efficient due to its exponential space complexity. Furthermore, we show that the space complexity can be significantly improved by a simple tweak. The algorithm then becomes equivalent to Chein’s algorithm, initially published in 1969. The second analyzed algorithm was published by Singh (2017), who proposes an extension of Formal Concept Analysis which handles vague (fuzzy interval valued) data and provides a method for computation of the associated concept lattice. We show that the same extension has been proposed before by Djouadi and Prade in 2009; that the proposed algorithm is incorrect and that it becomes an already known algorithm when we fix it. Additionally, we fix multiple errors in information about related literature committed by Singh.

Asymptotic results for lower exponential spacings

In this paper, we investigate distributional and asymptotic properties of lower exponential spacings. We find conditions under which the sequence of logarithmic lower spacings converges in probability and with probability one.

Approximation by Zygmund means in variable exponent Lebesque spaces

In the present work we investigate the approximation of the functions by the Zygmund means in variable exponent Lebesgue spaces. Here the estimate which is obtained depends on sequence of the best approximation in Lebesgue spaces with variable exponent. Also, these results were applied to estimates of approximations of Zygmund sums in Smirnov classes with variable exponent defined on simply connected domains of the complex plane.

Scalable Similarity-Consistent Deep Metric Learning for Face Recognition

With the development of deep learning, deep metric learning (DML) has achieved great improvements in face recognition. Specifically, the widely used softmax losses in the training process often bring large intra-class variations, and feature normalization is only exploited in the testing process to compute the pair similarities. To bridge the gap, we impose the intra-class cosine similarity between the features and weight vectors in softmax loss larger than a margin in the training step and extend it from four aspects. First, we explore the effect of a hard sample mining strategy. To alleviate the human labor of adjusting the margin hyper-parameter, a self-adaptive margin updating strategy is proposed. Then, a normalized version is given to take full advantage of the cosine similarity constraint. Furthermore, we enhance the former constraints to consider the intra-class and inter-class constraints simultaneously in the exponential feature projection space. The extensive experiments on the labeled face in the wild (LFW), youtube faces (YTF), and IARPA Janus benchmark A (IJB-A) datasets demonstrate that the proposed methods outperform the mainstream DML methods and approach the state-of-the-art performance.

Stellar mass black hole optimisation for utility mining

Major challenges in mining high utility itemsets from the transaction databases requires exponential search space and database-dependent minimum utility threshold. The search space is very large because of the large number of distinct items and size of the database. Data analysts need to specifying appropriate minimum utility thresholds for their data mining tasks though they may have no knowledge pertaining to their databases. To get rid of these problems, Stellar mass black hole optimisation (SBO) method is proposed to mine Top-K HUIs from the transaction database without specifying minimum utility threshold. To know the performance of SBO, the experiment results are compared with GA.

Time Series Analysis of Monthly Suicide Rates in West of Iran, 2006-2013.

Introduction:Iran's western provinces have higher suicide rate compared to the other provinces of the country. Although suicide rates fluctuate over time, suitable statistical models can describe their underlying stochastic dynamics.Methods:This study was conducted to explore the fluctuations of the monthly suicide rates in the most populated western province of Iran using exponential smoothing state space model to compute the forecasts. For this reason, the monthly frequencies of completed suicides were converted to rates per 100,000 and a state-space approach was identified and fitted to the monthly suicide rates. Diagnostic checks were performed to determine the adequacy of the fitted model.Results:A significant seasonal variation was detected in completed suicide with a peak in August. Diagnostic checks and the time series graph of the observed monthly suicide rates against predicted values from the fitted model showed that in the study period (from March 2006 to September 2013), the observed and predicted values were in agreement. Thus, the model was used to obtain the short-term forecasts of the monthly suicide rates.Conclusions:In this study, we had no significant trend but seasonal variations in the suicide rates that were identified. However, additional data from other parts of the country with longer duration are needed to visualize the reliable trend of suicide and identify seasonality of suicide across the country.

Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions

We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.

Mining Top-k Regular High-Utility Itemsets in Transactional Databases

Mining high-utility itemsets is an important task in the area of data mining. It involves exponential mining space and returns a very large number of high-utility itemsets. In a real-time scenario, it is often sufficient to mine a small number of high-utility itemsets based on user-specified interestingness. Recently, the temporal regularity of an itemset is considered as an important interesting criterion for many applications. Methods for finding the regular high utility itemsets suffers from setting the threshold value. To address this problem, a novel algorithm called as TKRHU (Top k Regular High Utility Itemset) Miner is proposed to mine top-k high utility itemsets that appears regularly where k represents the desired number of regular high itemsets. A novel list structure RUL and efficient pruning techniques are developed to discover the top-k regular itemsets with high profit. Efficient pruning techniques are designed for reducing search space. Experimental results show that proposed algorithm using novel list structure achieves high efficiency in terms of runtime and space.

The Opial condition in variable exponent sequence spaces l_p(.) with applications

In this work, we show an analogue to the Opial property for the coordinate-wise convergence in the variable exponent sequence space. This property allows us to prove a fixed point theorem for the mappings which are nonexpansive in the modular sense.

Optimal Homotopy Analysis of MHD Natural Convection Flow of Thixotropic Fluid under Subjection of Thermal Stratification: Boundary Layer Analysis

In this article, the model of a non-Newtonian fluid (Thixotropic) flow past a vertical surface in the presence of exponential space and temperature dependent heat source in a thermally stratified medium is studied. It is assumed that free convection is induced by buoyancy and exponentially decaying internal heat source across the space. The dynamic viscosity is taken to be constant and thermal conductivity of this particular fluid model is assumed to vary linearly with temperature. Thermal stratification has been properly incorporated into the governing equation so that its effect can be revealed and properly reported. The governing partial differential equations describing the model are transformed and parameterized to a system of non-linear ordinary differential equation using similarity transformations. Approximate analytic solutions were obtained by adopting Optimal Homotopy Analysis Method (OHAM). The results show that for both cases of non-Newtonian parameters (Thixotropic) (K1=K2=0 & K1=K2=1.0), increasing stratification parameters, relate to decreasing in the heat energy entering into the fluid region and thus reducing the temperature of the Thixotropic fluid as it flows.

Mixed convective radiative flow of vicoelastic liquid subject to space dependent internal heat source and chemical reaction

Present study addresses Soret and Dufour effects in mixed convection MHD flow of viscoelastic liquid with chemical reaction. Flow induced by an exponential stretching sheet is addressed in the presence of magnetic field. Energy expression is modelled by exponential space dependent internal heat source, thermal radiation, and convective condition. Relevant problems are modelled by employing boundary-layer concept. The partial differential systems are reduced to ordinary differential systems, and problem is solved by homotopic technique. Physical insight of results is arranged by graphs and tables.

The bullet problem with discrete speeds

Bullets are fired from the origin of the positive real line, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that a bullet with the second largest speed survives with positive probability, while a bullet with the smallest speed does not. This also holds for exponential spacings between firing times. Our results imply that the middle-velocity particle survives with positive probability in a two-sided version of the bullet process with three speeds known to physicists as ballistic annihilation.

Characterization of generalized Orlicz spaces

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

TPM

With the rapid development of location-based social networks (LBSNs), spatial item recommendation has become an important way of helping users discover interesting locations to increase their engagement with location-based services. The availability of spatial, temporal, and social information in LBSNs offers an unprecedented opportunity to enhance the spatial item recommendation. Many previous works studied spatial and social influences on spatial item recommendation in LBSNs. Due to the strong correlations between a user’s check-in time and the corresponding check-in location, which include the sequential influence and temporal cyclic effect, it is essential for spatial item recommender system to exploit the temporal effect to improve the recommendation accuracy. Leveraging temporal information in spatial item recommendation is, however, very challenging, considering (1) when integrating sequential influences, users’ check-in data in LBSNs has a low sampling rate in both space and time, which renders existing location prediction techniques on GPS trajectories ineffective, and the prediction space is extremely large, with millions of distinct locations as the next prediction target, which impedes the application of classical Markov chain models; (2) there are various temporal cyclic patterns (i.e., daily, weekly, and monthly) in LBSNs, but existing work is limited to one specific pattern; and (3) there is no existing framework that unifies users’ personal interests, temporal cyclic patterns, and the sequential influence of recently visited locations in a principled manner. In light of the above challenges, we propose a Temporal Personalized Model ( TPM ), which introduces a novel latent variable topic-region to model and fuse sequential influence, cyclic patterns with personal interests in the latent and exponential space. The advantages of modeling the temporal effect at the topic-region level include a significantly reduced prediction space, an effective alleviation of data sparsity, and a direct expression of the semantic meaning of users’ spatial activities. Moreover, we introduce two methods to model the effect of various cyclic patterns. The first method is a time indexing scheme that encodes the effect of various cyclic patterns into a binary code. However, the indexing scheme faces the data sparsity problem in each time slice. To deal with this data sparsity problem, the second method slices the time according to each cyclic pattern separately and explores these patterns in a joint additive model. Furthermore, we design an asymmetric Locality Sensitive Hashing (ALSH) technique to speed up the online top- k recommendation process by extending the traditional LSH. We evaluate the performance of TPM on two real datasets and one large-scale synthetic dataset. The performance of TPM in recommending cold-start items is also evaluated. The results demonstrate a significant improvement in TPM’s ability to recommend spatial items, in terms of both effectiveness and efficiency, compared with the state-of-the-art methods.