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The International League Against Epilepsy ( ILAE) presents a revised operational classification of seizure types. The purpose of such a revision is to recognize that some seizure types can have either a focal or generalized onset, to allow classification when the onset is unobserved, to include some missing seizure types, and to adopt more transparent names. Because current knowledge is insufficient to form a scientifically based classification, the 2017 Classification is operational (practical) and based on the 1981 Classification, extended in 2010. Changes include the following: (1) 'partial' becomes 'focal'; (2) awareness is used as a classifier of focal seizures; (3) the terms dyscognitive, simple partial, complex partial, psychic, and secondarily generalized are eliminated; (4) new focal seizure types include automatisms, behavior arrest, hyperkinetic, autonomic, cognitive, and emotional; (5) atonic, clonic, epileptic spasms, myoclonic, and tonic seizures can be of either focal or generalized onset; (6) focal to bilateral tonic-clonic seizure replaces secondarily generalized seizure; (7) new generalized seizure types are absence with eyelid myoclonia, myoclonic absence, myoclonic-atonic, myoclonic-tonic-clonic; and (8) seizures of unknown onset may have features that can still be classified. The new classification does not represent a fundamental change, but allows greater flexibility and transparency in naming seizure types. [ABSTRACT FROM AUTHOR]

Generalized pustular psoriasis (GPP) is a multisystem disease with potentially life‐threatening adverse effects. As patients increasingly seek health information online, and as the landscape for GPP changes, the quality of online health information (OHI) becomes progressively more important. This paper is the first of its kind to examine the quality, comprehensiveness and readability of online health information for GPP. Similar to pre‐existing studies evaluating OHI, this paper examines 5 key search terms for GPP‐ 3 medical and 2 laymen. For each search term, the results were evaluated based on HONcode accreditation, an enhanced DISCERN analysis and a number of readability indices. Of the 500 websites evaluated, 84 (16.8%) were HONcode‐accredited. Mean DISCERN scores of all websites were 74.9% and 38.6% for website reliability and treatment sections, respectively, demonstrating key gaps in comprehensiveness and reliability of GPP‐specific OHI. Additionally, only 4/100 websites (4%) analysed for readability were written at the NIH‐recommended sixth‐grade level. Academic websites were significantly more difficult to read than governmental websites. This further exacerbates the patient information gap, particularly for patients with low health literacy, who may already be at higher risk of not receiving timely medical care. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to obtain some new trapezium type in-equalities essentially involving the class of harmonic convex functions and generalized fractional integrals. [ABSTRACT FROM AUTHOR]

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure. This paper investigates whether using a more general form of acceptance, namely a transition-based generalized Rabin automaton (TGRA), improves the model checking procedure. TGRAs can have significantly fewer states than TGBAs; however, the corresponding emptiness checking procedure is more involved. With recent advances in probabilistic model checking and LTL to TGRA translators, it is only natural to ask whether checking a TGRA directly is more advantageous in practice. We designed a multi-core TGRA checking algorithm and performed experiments on a subset of the models and formulas from the 2015 Model Checking Contest and generated LTL formulas for models from the BEEM database. While we found little to no improvement by checking TGRAs directly, we show how various aspects of a TGRA's structure influences the model checking performance. In this paper, we also introduce a Fin-less acceptance condition, which is a disjunction of TGBAs. We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata. [ABSTRACT FROM AUTHOR]

Discovering new chaotic maps is always essential for secure communication, cryptography, image encryption and decryption when pseudo-number generation is mandatory; however, it is still very fascinating to come across new complex dynamics of very simple maps exhibiting chaotic behavior. Despite the various forms already presented in the literature, we deal with the fractional forms of one-dimensional chaotic map with one system parameter; yet while generalization, two parameters were inserted to the map as the multiplier and the power. Therefore, in this paper, we present a novel and generalized version of a map exhibiting a strange behavior in discrete time and real number space, while detailed analyses regarding the new map with intervals of various parameters are also included. We mainly focus on a simple one-dimensional chaotic map and propose various instances with linear stability, bifurcation and Lyapunov analyses for each instance, to enhance the understanding of unstable fractional chaotic maps. It is found that the fractional map exhibits quasiperiodicity as well as periodic behavior for the smallest power parameter; while the chaotic states emerge for larger values. [ABSTRACT FROM AUTHOR]

Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse factorizations of two kinds of generalized k--Fibonacci matrices. We derive some useful identities of the k--Fibonacci sequence. We investigate the Cholesky factorization of the generalized symmetric k--Fibonacci matrix by using these identities. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution. [ABSTRACT FROM AUTHOR]

This paper presents five feature-enriched hardware-efficient mixed mode universal filter (UF) biquads using digitally programmable (DP) current conveyors (CC). Common features of proposed UFs include use of only two grounded capacitors, operation in all the four modes, realization of all the filter functions, independently programmable filter parameters and cascadability (last three features, however, are partially present in last UF). Besides all these features, the first proposed UF, designated as Generalized DPUF provides additional features such as reconfigurability, use of minimum input terminals, no component matching constraint and lesser parasitic effects. Although Generalized DPUF encompasses almost all the desirable features of any filter, it uses eight CCs for obtaining these. The need of eight CCs is justified by introducing remaining four programmable/non-programmable UFs. These additional UFs are designated as Derived UFs as they are obtained by the deletion of CCs of the Generalized DPUF. Proportionate reduction in features of Derived UFs with number of CCs proves the reasonability of eight CCs in Generalized DPUF. To further strengthen this fact, all the proposed UFs are compared with reported filters. Better/comparable performance of Generalized and reduced-performance Derived filters again justifies the need of eight CCs in Generalized UF. [ABSTRACT FROM AUTHOR]

Summary: Objective: We aim to identify people with epilepsy who are unlikely to reachieve a 12‐month remission within 2 years after experiencing a breakthrough seizure following an initial 12‐month remission. Methods: We apply a novel longitudinal discriminant approach to data from the Standard and New Antiepileptic Drugs study to dynamically predict the risk of a patient not achieving a second remission after a breakthrough seizure by combining both baseline covariates (collected at the time of breakthrough seizure) and follow‐up data. Results: The model classifies 83% of patients. Of these, 73% of patients (95% confidence interval [CI] = 58%‐88%) who did not achieve a second remission were correctly identified (sensitivity), and 84% of patients (95% CI = 69%‐96%) who achieved a second remission were correctly identified (specificity). The area under the curve from our model was 87% (95% CI = 80%‐94%). Patients who did not achieve a second remission were correctly identified on average after 10 months of observation postbreakthrough. Occurrence of seizures after breakthrough and the number of seizures experienced were the most informative longitudinal variables. These longitudinal profiles were influenced by the following baseline covariates: age at breakthrough seizure, presence of neurological insult, and number of antiepileptic drugs required to achieve first remission. Significance: Using longitudinal data gathered during patient follow‐up allows more accurate predictions than using baseline covariates in a standard Cox model. The model developed in this paper is a useful first step in developing a tool for identifying patients who develop drug resistance after an initial remission. [ABSTRACT FROM AUTHOR]

In a recent research, the quasi-likelihood estimation methodology was developed to estimate the regression effects in the Generalized BINMA(1) (GBINMA(1)) process. The method provides consistent parameter estimates but, in the intermediate computations, moment estimating equations were used to estimate the serial- and cross-correlation parameters. This procedure may not result optimal parameter estimates, in particular, for the regression effects. This paper provides an alternative simpler GBINMA(1) process based on multivariate thinning properties where the main effects are estimated via a robust generalized quasi-likelihood (GQL) estimation approach. The two techniques are compared through some simulation experiments. A real-life data application is studied. [ABSTRACT FROM AUTHOR]

The object of the present paper is to obtain a necessary and sufficient condition for a 3-dimensional generalized (k, µ)-contact metric manifold to be locally φ-symmetric in the sense of Takahashi and the condition is verified by an example. Next we characterize a 3-dimensional generalized (k, µ)-contact metric manifold satisfying certain curvature conditions on the concircular curvature tensor. Finally, we construct an example of a generalized (k, µ)-contact metric manifold to verify Theorem 1 of our paper. [ABSTRACT FROM AUTHOR]

In this paper, a three parameters generalization of the power Lindley distribution is introduced. This includes as special cases the power Lindley and Lindley distribution. The new distribution exhibits decreasing, increasing and bathtub hazard rate depending on its parameters. Several statistical properties of the distribution are explored. Then, a bivariate version of the proposed distribution is derived. Finally, three real data applications illustrate the performance of our proposed distribution. [ABSTRACT FROM AUTHOR]

In this paper we study the structure of optimal policies for periodic review inventory systems with concave ordering costs and general demand distributions. By extending the Scarf () model to systems with piecewise linear concave ordering costs, we show that, except for a bounded region, the generalized (s, S) policy is optimal. We do so by (a) introducing the notion of c‐convexity and (b) proving a conditional monotonicity property for the optimal order‐up‐to levels. We also provide conditions under which the generalized (s, S) policy is optimal for all regions of the state space. [ABSTRACT FROM AUTHOR]

The well-known Weibull distribution can be used to model the decreasing and unimodal failure rate quite standard in reliability and biological studies. It is also commonly adopted as baseline to generate new distributions from generalized classes. In this paper, we investigate the identifiability of the exponentiated generalized class of distributions and in particular the exponentiated generalized Weibull distribution. We also develop conditions under which the model becomes identifiable. To further illustrate the identifiability issue, we consider a simulation study, and an application is presented to illustrate the potentialities of the model with the new parameterization. [ABSTRACT FROM AUTHOR]

This companion paper to the introduction of the International League Against Epilepsy ( ILAE) 2017 classification of seizure types provides guidance on how to employ the classification. Illustration of the classification is enacted by tables, a glossary of relevant terms, mapping of old to new terms, suggested abbreviations, and examples. Basic and extended versions of the classification are available, depending on the desired degree of detail. Key signs and symptoms of seizures (semiology) are used as a basis for categories of seizures that are focal or generalized from onset or with unknown onset. Any focal seizure can further be optionally characterized by whether awareness is retained or impaired. Impaired awareness during any segment of the seizure renders it a focal impaired awareness seizure. Focal seizures are further optionally characterized by motor onset signs and symptoms: atonic, automatisms, clonic, epileptic spasms, or hyperkinetic, myoclonic, or tonic activity. Nonmotor-onset seizures can manifest as autonomic, behavior arrest, cognitive, emotional, or sensory dysfunction. The earliest prominent manifestation defines the seizure type, which might then progress to other signs and symptoms. Focal seizures can become bilateral tonic-clonic. Generalized seizures engage bilateral networks from onset. Generalized motor seizure characteristics comprise atonic, clonic, epileptic spasms, myoclonic, myoclonic-atonic, myoclonic-tonic-clonic, tonic, or tonic-clonic. Nonmotor (absence) seizures are typical or atypical, or seizures that present prominent myoclonic activity or eyelid myoclonia. Seizures of unknown onset may have features that can still be classified as motor, nonmotor, tonic-clonic, epileptic spasms, or behavior arrest. This 'users' manual' for the ILAE 2017 seizure classification will assist the adoption of the new system. [ABSTRACT FROM AUTHOR]

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension. [ABSTRACT FROM AUTHOR]

Cooperative None Orthogonal Multiple Access (C-NOMA) is a promising approach for 5G and beyond communication networks. Users will benefit from the full bandwidth of the channel without time constraints. NOMA’s features are incomplete without efficient power allocation that ensures power distribution among users fairly. Integrating power management (allocation) with Cooperative-NOMA (C-NOMA) may improve the system metrics. In addition, a physical layer security (PLS) is added to make the process of sending and receiving safe, and the system works in an integrated manner, preventing any interrupting or eavesdropping inside or outside the network. This paper demonstrates the user and channel performance of C-NOMA with Amplify-and-forward (AF) and Decode-and-forward (DF) approaches. The analysis is performed by varying the power allocation techniques to derive the best system configurations. The simulation results confirmed the analytic findings and showed that the proposed system outperforms orthogonal multiple access (OMA), conventional NOMA, and conventional cooperative NOMA, enhancing the performance metrics in terms of throughput, sum rate, and outage probability. The bit-error-rate (BER) of the far user can be identical to that of the near user if power allocation is properly set. All techniques excelled except for the fixed power allocation, which had the same BER. The Channel capacity and outage probability were also considered. A slight variation in the channel capacity in all the experiments for different numbers of users was found. The generalized power allocation for AF and DF models had the optimum channel capacity close to 14 bps/Hz. Moreover, far users always had a higher outage probability than near users and channels, and generalized power allocation was the highest outage probability technique when the transmit power was close to (4 dB).

Let 픛 be a class of groups. A group G is said to be minimal non-픛 if all proper subgroups of G are 픛-groups but G itself is not. The aim of this paper is to study the class of minimal non-FCn-groups, where FCn (n is a positive integer) is a class of generalized FC-groups introduced in [F. de Giovanni, A. Russo and G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J.28 (2002) 241-254]. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with a study of the thermoelastic diffusion problem with thermal relaxation in a two-dimensional elastic medium. The bounding surface (isothermal or insulated) of the half-space is taken to be traction free and subjected to a uniformly distributed thermal shock. The fundamental equations of generalized thermoelasticity with diffusion with one relaxation parameter in an elastic medium are obtained as a vector-matrix differential equation form in the Laplace-Fourier transform domain, which is then solved by the eigenvalue approach. A numerical technique is employed to obtain the solution in the physical domain. A comparison is made between the results obtained in a thermoelastic medium with and without diffusion at two different times. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the generalized b-equation ut - uxxt + (b + 1)u2ux = buxuxx + uxxx. For a given constant wave speed, we investigate the coexistence of multifarious exact nonlinear wave solutions including smooth solitary wave solution, peakon wave solution, smooth periodic wave solution, single singular wave solution and periodic singular wave solution. Not only is the coexistence shown, but the concrete expressions are given via phase analysis and special integrals. From our work, it can be seen that the types of exact nonlinear wave solutions of the generalized b-equation are more than that of the b-equation. Many previous results are turned to our special cases. Also, some conjectures and questions are presented. [ABSTRACT FROM AUTHOR]

Let R be a commutative Noetherian local ring, 픞 an ideal of R, and M a finitely generated generalized f-module. Let t be a positive integer such that $H_{{\frak a}}^t(M)\neq 0$ and t > dim M - dim M/픞M. In this paper, we prove that there exists an ideal 픟 ⊇ 픞 such that (1) dim M - dim M/픟M = t; and (2) the natural homomorphism $H_{{\frak b}}^i(M)\rightarrow H_{{\frak a}}^i(M)$ is an isomorphism for all i > t and it is surjective for i = t. Also, we show that if ${\rm Supp}_{R}(H_{{\frak a}}^i(M))$ is a finite set for all i < t, then there exists an ideal 픟 of R such that dim R/픟 ≤ 1 and $H_{{\frak b}}^i(M)\cong H_{{\frak a}}^i(M)$ for all i < t. [ABSTRACT FROM AUTHOR]

The work discusses a response to the alternating external field of a stochastic resonance (SR) within the framework of the three-state system non-Markovian renewal processes. In the present paper, we provide an alternative description of the situation within the framework of a generalized master Markovian equation. [ABSTRACT FROM AUTHOR]

A compact bordered Klein surface of algebraic genus p ≥ 2 has at most 12(p-1) automorphisms. Automorphism groups which attain this bound are called M*-groups. In this paper, firstly, we define generalized M*-groups. Then, we show that there is a relationship between the extended Hecke groups and generalized M*-groups. Finally, we prove that a generalized M*-groups G is supersoluble if and only if |G| = 4 · qr for q ≥ 3 prime number and for some positive integer r. [ABSTRACT FROM AUTHOR]

Generalized eigendecomposition (GED) plays a vital role in many signal-processing applications. In this paper, we will propose a new method for computing the generalized eigenvectors, which is on-line and resembles the RLS algorithm for Wiener filtering. We further present a proof to show convergence to the exact solution and simulations have shown that the algorithm is faster than most of the traditional methods. This algorithm belongs to the class of fixed-point algorithms and hence does not require any external step-size parameters like the gradient-based methods. Simulations are performed on synthetic data and compared with other algorithms found in literature. Finally we will demonstrate the application of GED in the design of a CDMA receiver for direct-sequence spread spectrum signals. [ABSTRACT FROM AUTHOR]

The study of multivariate distributions of order k, two of which are the multivariate negative binomial of order k and the multinomial of the same order, was introduced in Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1988). Multivariate distributions of order k. Statistics and Probability Letters 7(3):207-216.), and Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1990). Multivariate distributions of order k, part II. Statistics and Probability Letters 10(1):29-35.). Recently, an order k (or cluster) generalized negative binomial distribution and a multivariate negative binomial distribution were derived in Sen and Jain (Sen, K., Jain, R. (1996). Cluster generalized negative binomial distribution. In: Borthakur et al. A. C., Eds.; Probability Models and Statistics Medhi Festschrift, A. J., on the Occasion of his 70th Birthday. New Age International Publishers: New Delhi, 227-241.) and Sen and Jain (Sen, K., Jain, R. (1997). A multivariate generalized Polya-Eggenberger probability model-first passage approach. Communications in Statistics-Theory and Methods 26:871-884.), respectively. In this paper, all four distributions are generalized to a multivariate generalized negative binomial distribution of order k by means of an appropriate sampling scheme and a first passage event. This new distribution includes as special cases several known and new multivariate distributions of order k, and gives rise in the limit to multivariate generalized logarithmic, Poisson and Borel-Tanner distributions of the same order. Applications are indicated. [ABSTRACT FROM AUTHOR]

Cenobamate (CNB), ([(R)-1-(2-chlorophenyl)-2-(2H-tetrazol-2-yl)ethyl], is a novel tetrazole alkyl carbamate derivative. In November 2019, the Food and Drug Administration approved Xcopri®, marketed by SK Life Science Inc., (Paramus, NJ, USA) for adult focal seizures. The European Medicines Agency approved Ontozry® by Arvelle Therapeutics Netherlands B.V.(Amsterdam, The Neatherlands) in March 2021. Cenobamate is a medication that could potentially change the perspectives regarding the management and prognosis of refractory epilepsy. In this way, this study aims to review the literature on CNB's pharmacological properties, pharmacokinetics, efficacy, and safety. CNB is a highly effective drug in managing focal onset seizures, with more than twenty percent of individuals with drug-resistant epilepsy achieving seizure freedom. This finding is remarkable in the antiseizure medication literature. The mechanism of action of CNB is still poorly understood, but it is associated with transient and persistent sodium currents and GABAergic neurotransmission. In animal studies, CNB showed sustained efficacy and potency in the 6 Hz test regardless of the stimulus intensity. CNB was revealed to be the most cost-effective drug among different third-generation antiseizure medications. Also, CNB could have neuroprotective effects. However, there are still concerns regarding its potential for abuse and suicidality risk, which future studies should clearly assess, after which protocols should be changed. The major drawback of CNB therapy is the slow and complex titration and maintenance phases preventing the wide use of this new agent in clinical practice. [ABSTRACT FROM AUTHOR]

Most traditional AC/AC power converters suffer from power quality problems and multi-stage power conversion losses. The rectifier and inverter-based AC/AC converter topology not only increases multi-stage power conversion losses, but also increases the volume, weight, and cost, and decreases the longevity of the converter due to the DC-link capacitor, line filter and electromagnetic interference (EMI) filter. High-frequency (about 10 kHz) switching advanced pulse width modulation techniques are generally used in order to compensate the power quality problems, which increase the switching losses and introduce the EMI problems. In this paper, a new generalized step-down single-stage line-frequency switching AC/AC power converter topology is proposed. The proposed converter uses line-frequency switching, and does not require any pulse width modulation techniques. The proposed topology offers promising performances in terms of lower order harmonics, total harmonic distortion, the elimination of DC-link capacitors and EMI filters, and switching losses. The circuit was designed and simulated in a MATLAB/Simulink environment. A scaled-down laboratory prototype of the proposed topology was developed in order to validate the feasibility. The experimental and simulation results reveal the feasibility of the proposed generalized step-down single-stage converter topology, and its excellent features. [ABSTRACT FROM AUTHOR]

• A new State Estimation model uses Generalized Correntropy as quality criterion. • A new algorithm based on the Interior Point Method assures convergence. • Multiple gross errors are dealt with naturally, better than in classical models. • Higher robustness (smaller risk of wrong estimation) confirmed in extensive tests. • Gross errors in critical measurements and leverage points dealt with successfully. This paper provides an answer to the problem of State Estimation (SE) with multiple simultaneous gross errors, based on Generalized Error Correntropy instead of Least Squares and on an interior point method algorithm instead of the conventional Gauss–Newton algorithm. The paper describes the mathematical model behind the new SE cost function and the construction of a suitable solver and presents illustrative numerical cases. The performance of SE with the data set contaminated with up to five simultaneous gross errors is assessed with confusion matrices, identifying false and missed detections. The superiority of the new method over the classical Largest Normalized Residual Test is confirmed at a 99% confidence level in a battery of tests. Its ability to address cases where gross errors fall on critical measurements, critical sets or leverage points is also confirmed at the same level of confidence. [ABSTRACT FROM AUTHOR]

The matchless properties possessed by biological composites such as nacre, bone, turtle, armadillo, and spider silk are a great inspiration to humankind which lead to the mimicking of their geometric and material features to simulate synthetic so-called bio-inspired composites. Bio-inspired composites are often considered an ideal candidate in the field of light and innovative structures, which the world is in need of. In order to develop a bio-inspired composite with fine mechanical properties, it is required to study all the possible factors which are responsible for the superior mechanical properties of a biological composite. The hierarchical arrangement and the staggering pattern of the platelets inside the matrix are major factors affecting the final properties of such composite materials. The generalization of parameters in a hierarchical structure could be beneficial in finding out the optimum parameters responsible for the maximum desirable mechanical properties in a bio-inspired composite. In this paper, we formulate a novel generalized model for a stairwise staggered (which is regarded as one of the patterns mostly found in nature due to its optimized properties) two hierarchical bio-inspired composite, and we optimize the model for a tailored design according to the stiffness, strength, and toughness requirements. The developed model can evaluate self-similar as well as non-self-similar configurations, and the analytical results from the studies show a good agreement when compared with the models of specific known designs from the literature. Also, the ternary plots obtained from optimization show that the number of platelets in a period at the first and second levels of hierarchy are the key parameters other than the volume fractions and the critical aspect ratios, controlling the final properties of the two hierarchical composites.

The article is devoted to the noncommutative integration of a diffusion partial differential equation (PDE). Its generalizations are also studied. This is motivated by the fact that many existing approaches for solutions of PDEs are based on evolutionary operators obtained as solutions of the corresponding stochastic PDEs. However, this is restricted to PDEs of an order not higher than 2 over the real or complex field. This article is aimed at extending such approaches to PDEs of an order higher than 2. For this purpose, measures and random functions having values in modules over complexified Cayley–Dickson algebras are investigated. Noncommutative integrals of hypercomplex random functions are investigated. By using them, the noncommutative integration of the generalized diffusion PDE is scrutinized. Possibilities are indicated for a subsequent solution of higher-order PDEs using their decompositions and noncommutative integration. [ABSTRACT FROM AUTHOR]

An Interval-Valued Trapezoidal Intuitionistic Fuzzy Number (IVTrlFN) is a special case of an Intuitionistic Fuzzy Set (IFS), which is defined on a real number set. From a geometric viewpoint, the expectation and expectant score of an IVTrlFN are defined using the notion of a b ary center, and a new method is developed to rank IVTrlFNs. Hereby, some generalized aggregation operators of IVTrIFNs are defined, including the generalized ordered weighted averaging operator and the generalized hybrid weighted averaging operator, which are employed to solve multi-attribute group decision making problems. Using the weighted average operator of IVTrIFNs, the attribute values of alternatives are integrated into the individual comprehensive ratings, which are further aggregated into the collective one by the generalized hybrid weighted averaging operator of IVTrIFNs. The ranking orders of alternatives are then generated according to the expectation and expectant score of the collective comprehensive ratings of alternatives. A numerical example is examined to demonstrate the applicability and implementation process of the decision method proposed in this paper. [ABSTRACT FROM AUTHOR]

Abstract The well-known Weibull distribution can be used to model the decreasing and unimodal failure rate quite standard in reliability and biological studies. It is also commonly adopted as baseline to generate new distributions from generalized classes. In this paper, we investigate the identifiability of the exponentiated generalized class of distributions and in particular the exponentiated generalized Weibull distribution. We also develop conditions under which the model becomes identifiable. To further illustrate the identifiability issue, we consider a simulation study, and an application is presented to illustrate the potentialities of the model with the new parameterization.

The similarity solutions of the steady-state (SS) magneto-hydrodynamics (MHD) flow over a semi infinite surface were currently studied in the literature. It is worthy to mention that the works done in the literature were concerned with studying the cases when the boundary conditions of the directed and perpendicular velocities at the surface are taken constants or linear in the space variable. Here, the objective of present work is to investigate the behavior of similarity solutions of the SS-MHD equation for in-homogeneous kinematic viscosity and arbitrary boundary conditions at the stretching surface. The exact solutions are obtained by implementing the extended and generalized unified methods. It is found that, multiple SS-MHD flow structures, over an infinite and semi-infinite surfaces, occur. This arises from the presence of arbitrary functions which are embedded in the solutions. In the case of semi-infinite surface the boundary condition is used. Highly oscillatory tlow over an infinite surface and zig-zag flow over semi infinite surface are observed. The effects of varying the induced magnetic field and the viscosity of the stretching and perpendicular velocities are investigated. It is found that, over semi-infinite surface, the magnitude of the stretching velocity raises, while the perpendicular velocity decreases, significantly with the strength of the field. The inverse statement hods when varying the magnitude of the viscosity. A novel approach for analyzing the stability of the steady flow solution is proposed and used here. [ABSTRACT FROM AUTHOR]