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Many industrial facilities involve splitting production systems of different complexities and arrangements. The accurate and efficient evaluation of the associated performance measures is, therefore, of great importance. This challenging task can be accomplished by applying mathematical models of production system engineering at different intricacies. This paper presents the development and application of the analytical approach to splitting production systems modelling. The same problem is also addressed using the finite state method as a semi-analytical model. Several theoretical examples were considered to validate the finite state method that proved to be quite efficient and accurate. Finally, the developed modelling approach was applied in the case of a wood-processing facility. The obtained results were validated successfully against the acquired factory-floor data. [ABSTRACT FROM AUTHOR]

The buffer allocation problem in production lines is an NP-hard combinatorial optimisation problem. This paper proposes a new hybrid optimisation approach (using simulation) relying on genetic algorithm (GA) and finite perturbation analysis (FPA). Unlike the infinitesimal perturbation analysis, which deals with small (infinitesimal variation) perturbations for estimating gradients of the performance measure, FPA deals with larger (finite) or more lasting perturbations. It is an extension specifically dedicated to discrete decision variables and applicable to most discrete-event dynamic systems. The proposed method allows a global search using GA, with refinement in specific solution-space regions using FPA. The main objective is to maximise the average production rate of a production line with unreliable machines, by allocating the total buffer capacity in locations between machines. Extensive numerical experiments show that: (1) the proposed hybrid GA-FPA method clearly outperforms the state-of-the-art methods from the literature; (2) combining FPA and GA is beneficial when compared to employing GA or FPA independently. [ABSTRACT FROM AUTHOR]

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset. [ABSTRACT FROM AUTHOR]

This paper examines serial production lines with unreliable non-identical parallel machines at each workstation and intermediate buffers with finite capacities. All machines are assumed to have exponential service times, times to failure and repair times. An efficient decomposition technique is introduced for the performance evaluation of such lines. Rather than replacing each parallel-machine workstation with an equivalent single-server workstation, the main contribution of this paper is the presentation of a direct approach to derive and apply decomposition equations directly for every parallel machine at each workstation. Experimental results indicate that such a method can provide a computationally efficient algorithm to analyse large serial unreliable multi-server production lines with a good accuracy compared against simulation and other available methods. [ABSTRACT FROM AUTHOR]

Although there is a broad literature on capacity management, there has been only limited attention on how to support short-term capacity control decisions, especially in high-variety make-to-order shops. While finite loading has been identified as a potential means of guiding capacity adjustments, the actual performance impact of this solution has not been adequately assessed. Using a simulation model of a make-to-order job shop, we compare the performance impact of four different forward and backward finite loading methods and a load trigger method recently presented in the literature. Results confirm the potential of finite loading to improve performance when compared to a general capacity increase. Yet all four methods are outperformed by the load trigger method. The capacity adjustments made under finite loading methods are determined by individual jobs and their properties. This may lead to no adjustments despite an overload period (e.g. if a job has a long due date but only one overload station in its routing) or to unnecessary adjustments when there is no overload (e.g. if a large job has a tight due date). This finding draws into question the use of finite loading altogether and reinforces the importance of the load trigger method. [ABSTRACT FROM AUTHOR]

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake. [ABSTRACT FROM AUTHOR]

For any positive integer 2n and any positive integer m, l, a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2 n − 1) (m + l + 1) + 1 eigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n (m + l + 2). [ABSTRACT FROM AUTHOR]

A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the L 1 -distance of a function of the probability generating function of the model under the null hypothesis and that of the random variable actually generating data, when the latter belongs to a suitable wide class of alternatives. The test statistic has a rather simple form and it is asymptotically normally distributed under the null hypothesis, allowing a straightforward implementation of the test. Moreover, the test is consistent for alternative distributions belonging to the class, but also for all the alternative distributions whose probability of zero is different from that under the null hypothesis. Thus, the use of the test is proposed and investigated also for alternatives not in the class. The finite-sample properties of the test are assessed by means of an extensive simulation study. [ABSTRACT FROM AUTHOR]

We establish asymptotic and finite sample properties of the Hill and Harmonic Moment estimators applied to heavy-tailed data contaminated by errors. We formulate conditions on the errors and the number of upper order statistics under which these estimators continue to be asymptotically normal. We specify analogous conditions which must hold in finite samples for the confidence intervals derived from the asymptotic normal distribution to be reliable. In the large sample analysis, we specify conditions related to second-order regular variation and divergence rates for the number of upper order statistics, k, used to compute the estimators. In the finite sample analysis, we examine several data-driven methods of selecting k, and determine which of them are most suitable for confidence interval inference. The results of these investigations are applied to interarrival times of internet traffic anomalies, which are available only with a round-off error. [ABSTRACT FROM AUTHOR]

This paper presents a novel estimation approach for cumulative link models, based on median bias reduction. The median bias reduced estimator is obtained as solution of an estimating equation based on an adjustment of the score. It allows to obtain higher-order median centering of maximum likelihood estimates without requiring their finiteness. The estimator is equivariant under componentwise monotone reparameterizations and the method is effective in preventing boundary estimates. Through simulation studies and an application, we compare the median bias reduced estimator with the two main competitors, the maximum likelihood and the mean bias reduced estimators. The method is seen to be highly successful in achieving median centering and shows remarkable properties under reparameterizations related to effect measure. [ABSTRACT FROM AUTHOR]

Let R be a ring and X a complex of R-modules. We give some characterizations of the dimension of X related to special Gorenstein projective precovers. Let R be a ring such that (G P , G P ⊥) forms a cotorsion pair cogenerated by a set, where G P denotes the category consisting of all Gorenstein projective R-modules. Then the dimension related to special Gorenstein projective precovers Gppd (X) is equal to the infimum of the set { n ∈ Z | there exists a complete Gorenstein projective resolution of X T → σ G → X such that σi is bijective for each i ≥ n }. Forthmore, if Gppd (X) is finite and n an integer then Gppd (X) ≤ n if and only if Ext G P i (X , Q) = 0 for any i > n and any projective R-module Q, where Ext G P i (− , −) is the relative cohomology functor. [ABSTRACT FROM AUTHOR]

Let R ⊂ S be a Frobenius extension of rings and M an S-complex. It is proven that if the Gorenstein projective (injective) dimension of M as an S-complex is finite, then the Gorenstein projective (injective) dimension of M as an S-complex equals the Gorenstein projective (injective) dimension of M as an R-complex. As a corollary one has that if the projective (injective) dimension of M as an S-complex is finite, then the projective (injective) dimension of M as an S-complex equals the projective (injective) dimension of M as an R-complex. This statement extends a known result of Nakayama and Tsuzuku. [ABSTRACT FROM AUTHOR]

In this paper we consider the monoid D P S n of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of D P S n . We also describe Green's relations of D P S n and calculate its cardinal. [ABSTRACT FROM AUTHOR]

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite Rees matrix semigroups, in particular, 0-simple semigroups, and their mutually annihilating unions. [ABSTRACT FROM AUTHOR]

A finite periodic structure consisting of active functionally graded (FG) metamaterial bars is proposed, and the active FG metamaterial bar is constructed by a FG host bar and equidistantly distributed piezoelectric actuator/sensor groups. An analytical model is presented for the dynamic behavior of the finite periodic FG metamaterial structure. The calculation accuracy for present analytical model is validated by the finite element method (FEM). The results demonstrate that the width and location of band gaps for the periodic FG metamaterial structure can be tuned by adjusting the feedback control gain of the controller and designing the gradient index. [ABSTRACT FROM AUTHOR]

This paper initially presents bounds for the joint tail and the conditional tails of the backward and forward recurrence times. Using these bounds, we deliver an improvement to the lower bound for the renewal function given by Brown [Inequalities for distributions with increasing failure rate. In: Gelfand AE, editors. Contributions to the theory and applications of statistics, a volume in honour of Herbert Solomon. Orlando, FL: Academic; 1987. p. 3–17] for IFR inter-arrival times. Finally, this paper proposes a renewal type equation for the expected number of renewals in (t , t + h ] and, under certain conditions, improves Lorden's [On excess over the boundary. Ann Math Stat. 1970;41(2):520–527] well-known general upper bound for the expected number of renewals in (t , t + h ]. [ABSTRACT FROM AUTHOR]

The estimation algebra plays an important role in classification of finite dimensional filters. When finite dimensional estimation algebra has maximal rank, Yau et al. [Yau (2003). Complete classification of finite-dimensional estimation algebras of maximal rank. International Journal of Control, 76(7), 657–677; Yau & Hu (2005). Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state-space dimension and Mitter conjecture. International Journal of Control, 78(10), 689–705.] have proved that η must be a degree 2 polynomial. In this paper, we study the structure of finite dimensional exact estimation algebra with state dimension 3 and rank 2. We establish a sufficient and necessary condition for estimation algebra with nonmaximal rank to be finite dimensional. Importantly, in the new filtering system, η needs not to be a degree 2 polynomial and can be of any degree 4 n 1 + 2 , n 1 ∈ Z + . It is the first time to systematically analyse nonmaximal rank exact estimation algebra in which η is a polynomial of any degree 4 n 1 + 2 , n 1 ∈ Z + . For Riccati-type equation, estimates have been done from the viewpoints of both classical solution and weak solution respectively. Finally, finite dimensional filters of Benés type are constructed successfully. [ABSTRACT FROM AUTHOR]

We introduce the Hochschild extensions of dg algebras, which are A ∞ -algebras. We show that all exact Hochschild extensions are symmetric Hochschild extensions, more precisely, every exact Hochschild extension of a finite dimensional complete typical dg algebra is a symmetric A ∞ -algebra. Moreover, we prove that the Koszul dual of trivial extension is Calabi-Yau completion and the Koszul dual of exact Hochschild extension is deformed Calabi-Yau completion, more precisely, the Koszul dual of the trivial extension of a finite dimensional complete dg algebra is the Calabi-Yau completion of its Koszul dual, and the Koszul dual of an exact Hochschild extension of a finite dimensional complete typical dg algebra is the deformed Calabi-Yau completion of its Koszul dual. [ABSTRACT FROM AUTHOR]

In this article, we study the notion of central extensions of Leibniz n-algebras relative to n-Lie algebras to study properties of Schur Lie -multiplier and Lie -covers on Leibniz n-algebras. We provide a characterization of Lie -perfect Leibniz n-algebras by means of universal Lie -central extensions. It is also provided some inequalities on the dimension of the Schur Lie -multiplier of Leibniz n-algebras. Analogue to Wiegold and Green results on groups or Moneyhun results on Lie algebras, we provide upper bounds for the dimension of the Lie -commutator of a Leibniz n-algebra with finite dimensional Lie -central factor, and also for the dimension of the Schur Lie -multiplier of a finite dimensional Leibniz n-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions. [ABSTRACT FROM AUTHOR]

The finite frequency domain H ∞ consensus control problem of neutral multi-agent systems with the input delay is investigated in this paper for the first time. According to the linear transformation, the problem of H ∞ consensus is converted into a set of H ∞ stability problems. Through the Lyapunov theory, combined with the time-delay interval decomposition method, a less conservative controller design method for the state feedback controller is presented. And the obtained controller can ensure closed-loop multi-agent systems to fulfil the consensus. Utilizing the generalised Kalman-Yakubovich-Popov (GKYP) lemma, the sufficient condition is derived for multi-agent systems achieving the H ∞ performance in the finite frequency domain (FFD). Then, via the orthogonal spatial information of the input matrix, the conservativeness of obtained design approach is further declined. Moreover, the design method with less conservativeness is proposed for the dynamic output feedback controller. Finally, a numerical case and a multi-pendulum system controlled by the multi-motor system are presented in this paper to demonstrate the availability and applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper we provide further studies of Fenchel duality theory in the general framework of locally convex topological vector (LCTV) spaces. We prove the validity of the Fenchel strong duality under some qualification conditions via generalized relative interiors imposed on the epigraphs and the domains of the functions involved. Our results directly generalize the classical Fenchel–Rockafellar theorem on strong duality from finite dimensions to LCTV spaces. [ABSTRACT FROM AUTHOR]

Let M n be the variety generated by all monoids of order n. It was known that M n is finitely based if n ⩽ 4 and non-finitely based if n ⩾ 6. However, the finite basis problem for M 5 remained open. In this paper, we show that the variety M 5 is finitely based by giving a finite identity basis. Therefore, M n is finitely based if and only if n ⩽ 5. [ABSTRACT FROM AUTHOR]

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous work of ours. We give several equivalent descriptions and use them to establish properties like residual finiteness, the Haagerup property or a smash product decomposition. [ABSTRACT FROM AUTHOR]

The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation criterion is minimized. We prove that the resultant combined-kernel estimator achieves the smallest possible asymptotic aggregate squared error. The superiority of the new estimator over estimators based on widely accepted conventional bandwidth choices in finite samples is demonstrated in a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

In conventional finite element–Lagrangian methods, the dynamics model of a flexible robot is usually formulated based on a critical assumption that the kinetic energy of an element is approximately calculated with an integral of mass point energy. Since the energy integral is implicit, the formulation of the dynamics model is also very complex and implicit. Hence, this article develops a new mathematical approach for the dynamic modeling of a general flexible/rigid robot. The proposed method is more comprehensive and efficient in comparison with the previous ones because it no longer requires the calculation of the symbolic integrals and the implicit expressions of the elemental and global mass matrices. Besides, the proposed approach is applicable for both the flexible robots and the hybrid flexible/rigid robots. To validate the proposed method, numerical simulations and experimental results are presented. [ABSTRACT FROM AUTHOR]

In this article, a new finite strip formulation based on Carrera unified formulation (CUF) is developed to perform the free vibration analysis of cross- and angle-ply composite laminated plates. The FSM discretizes the plate by a number of strips which are connected through the nodal lines, and calls for use of simple polynomial shape functions in one direction of the plane of strips and harmonic series in the other. In the present formulation, all three components are considered for displacement field in each nodal line. CUF approach which is obtained in the framework of the Carrera unified formulation, permits stating the unknown variables as a set of the function expansions depending on the thickness coordinate and the corresponding variable depending on the in-plane coordinates. Several numerical examples for the analysis of laminated plates are presented and the effect of the number of strips, order of expansion, different relative thickness ratio and various boundary conditions are demonstrated. [ABSTRACT FROM AUTHOR]

The aim of this work is to show the consistency of all systems of non-homogeneous linear difference equations of the form φ (x n + 1) = x n + v 0 , where φ ∈ End k ⁡ (V) is a finite potent endomorphism of an arbitrary vector space V and v 0 ∈ V. An algorithm to compute the set of solutions of these systems is given. In particular, the method offered is valid for computing the explicit solutions of the system of non-homogeneous difference equations A (x n + 1) = x n + b , with A being a finite square matrix. [ABSTRACT FROM AUTHOR]

A tensor v is the sum of at least rank ⁡ (v) elementary tensors. In addition, a 'border rank' is defined: rank _ (w) = r holds if r is the minimum integer such that w is a limit of rank-r tensors. Usually, the set of rank-r tensors is not closed, i.e. tensors with r = rank _ (w) < rank ⁡ (w) may exist. It is easy to see that in such a case the representation of rank-r tensors v contains diverging elementary tensors as v approaches w. In a first part, we recall results about the uniform strength of the divergence in the case of general nonclosed tensor formats (restricted to finite dimensions). The second part discusses the r-term format for infinite-dimensional tensor spaces. It is shown that the general situation is very similar to the behaviour of finite-dimensional model spaces. The third part contains the main result: it is proved that in the case of rank _ (w) = 2 < rank ⁡ (w) the divergence strength is ≳ ε − 1 / 2 , i.e. if ‖ v − w ‖ < ε and rank ⁡ (v) ≤ 2 , the parameters of v increase at least proportionally to ε − 1 / 2. [ABSTRACT FROM AUTHOR]

A novel analytical approach to investigate the finite bending of hyperelastic laminated beams is presented. Two different nonlinear material models are taken into account, which are the compressible Mooney-Rivlin for rubberlike mediums and the Saint Venant-Kirchhoff for less deformable materials. The anticlastic bending is included in the formulation and the analytical expression of the transverse radius of curvature is presented. The stress analysis is performed in each layer separately, by considering the actual stored energy function of the constituents, in both Lagrangian and Eulerian frameworks. The finite bending of a sandwich beam is investigated in terms of stresses and stretches. [ABSTRACT FROM AUTHOR]

In this work, we establish two new self-adaptive parallel algorithms to solve the generalized split common fixed point problem which is to find a point which belongs to the intersection of finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. Under suitable assumptions, the weak and strong convergence theorems are analysed. The obtained results generalize and improve the recent results announced by many other authors in the framework of split inverse problem. As a direct consequence of our two main algorithms, we obtain several new algorithms. Preliminary numerical experiments are provided to illustrate the efficiency and implementation of our new methods and also to compare with others. [ABSTRACT FROM AUTHOR]

Due to reduced energy efficiency and productivity loss caused by fouled heat exchangers in industrial plants there is an obvious need for detection of fouling formation. Based on continuously measured temperatures and flow rates collected from the refinery plant history database, a semi-empirical number of transfer units (NTU) model and neural network-based models are developed. In order to confirm the reliability of proposed fouling factor calculation, the entire procedure was performed by developing a dynamic nonlinear finite impulse response (NFIR) model. Developed models are intended for fouling detection for industrial shell and tube heat exchangers. The performance criteria of developed models together with residual monitoring indicate that not only neural networks but the NTU and NFIR models effectively detect fouling formation. [ABSTRACT FROM AUTHOR]

We study the notion of the Schur multiplier of a pair (N, L) of Lie superalgebras and obtain some upper bounds concerning dimensions. Moreover, we characterize the pairs of finite dimensional (nilpotent) Lie superalgebras for which for t = 0; 1, where dim N = (m|n). [ABSTRACT FROM AUTHOR]

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for this class of inverse problems. [ABSTRACT FROM AUTHOR]

A hybrid particle/finite volume algorithm has been formulated for zone-adaptive modelling of turbulent reactive flows to achieve both high fidelity in predictions and high computational efficiency. Specifically, a computationally economical species transport model via finite volume algorithm is employed as the base model for the whole computational domain, while the advanced transported probability density function (TPDF) method via Lagrangian particle tracking is employed only for regions with intense turbulence-chemistry interaction. The 'PDF regions' can be updated dynamically based on local flow and flame characteristics, and are compatible with complex geometric structures such as separated multi blocks, non-convex, and multi-connected regions. A two-way particle/finite volume submodel coupling is formulated to ensure the composition consistency in submodels in the PDF regions and to impose the correct interface conditions for composition and mass flow rate on the boundary of the PDF regions. The spatial partition and particle algorithms for time-varying PDF regions are demonstrated and the convergence characteristics of the adaptive modelling are investigated specifically for the variation of statistical error and bias with the number of particles per cell. The proposed zone-adaptive hybrid particle/finite volume algorithm has been numerically validated in a turbulent hydrogen/air non-premixed jet flame. It is shown that the predictions from zone-adaptive modelling are almost identical to those of stand-alone TPDF, illustrating the preservation of prediction accuracy but with significantly less computational cost. [ABSTRACT FROM AUTHOR]

We propose consistent and efficient robust different time-scales estimators to mitigate the heavy-tail effect of high-frequency financial data. Our estimators are based on minimising the Huber loss function with a suitable threshold. We show these estimators are guaranteed to be robust to measurement noise of certain types and jumps. With only finite fourth moments of the observation log-price data, we develop the sub-Gaussian concentration of our estimators around the volatility. We conduct the simulation studies to show the finite sample performance of the proposed estimation methods. The simulation studies imply that our methods are also robust to financial data in the presence of jumps. Empirical studies demonstrate the practical relevance and advantages of our estimators. [ABSTRACT FROM AUTHOR]

I respond to objections from three rigorous readers challenging me to detail in what sense Sellars is a transcendental philosopher, as well as to defend the claim that 'picturing' is crucial to his account of intentionality. This further involves defending the tenability of transcendental phenomenalism and arguing against scepticism about picturing. Finally, this involves the question of whether the results of transcendental analyses undermine the legitimacy of the Manifest Image, and, consequently, to say what knowledge about phenomena can mean in the succession of conceptual frameworks. [ABSTRACT FROM AUTHOR]

In this paper, we propose clustering algorithms based on finite mixture and infinite mixture models of exponential approximation to the Multinomial Generalized Dirichlet (EMGD), Multinomial Beta-Liouville (EMBL) and Multinomial Shifted- Scaled Dirichlet (EMSSD) with Bayesian inference. The finite mixtures have already shown superior performance in real data sets clustering using the Expectation--Maximization approach. The proposed approaches in this paper are based on a Monte Carlo simulation technique namely Gibbs sampling algorithm including an additional Metropolis--Hastings step, and we utilize exponential family conjugate prior information to construct their posterior relying on Bayesian theory. Furthermore, we also present the infinite models based on Dirichlet processes, which results in clustering algorithms that do not require the specification of the number of mixture components to be given in advance and selects it in a principled manner. The performance of our Bayesian approaches was evaluated in some challenging real-world applications concerning text sentiment analysis, fake news detection, and human face gender recognition. [ABSTRACT FROM AUTHOR]

We introduce the notion of Krull super-dimension of supermodules over certain super-commutative Noetherian super-rings. We investigate how this notion relates to the notion of odd regular sequence due T. Schmitt and how it behaves with respect to the transition to the graded and bigraded super-modules and super-rings associated with the original ones. We also apply these results to the super-dimension theory of superschemes of finite type and their morphisms. [ABSTRACT FROM AUTHOR]

In this article, we introduce the concept of parallel Krull dimension of a module (briefly, p.Krull dimension), which is Krull-like dimension extension of the concept of DCC on poset of submodules parallel to itself. Using this concept, we extend some basic results about modules with this dimension. In particular, we show that an R-module M has Krull dimension if and only if it has homogeneous parallel Krull dimension with finite Goldie dimension and these two dimensions for M coincide. Furthermore, we define the concept of α-DICCP and we prove that M is an α-DICC module if and only if M is an α-DICCP module with finite Goldie dimension. Also, after defining of p-Artinian (resp., p-Noetherian) modules, we prove that if R is semiprime, p-Artinian commutative ring with finite Goldie dimension, then R is a Goldie ring. [ABSTRACT FROM AUTHOR]

This study presents car crash-induced neck injury trends in response to variations in three impact variables: velocity (10 − 45 mph; 16.1 − 72.4 km/h), location (front, rear, near side, and far side), and angle (-45° to 45°). By employing a combined finite element (FE)-mathematical surrogate modeling approach, the number of necessary FE crash simulations was significantly reduced. Each motor vehicle collision (MVC) case was simulated with LS-DYNA software, and the extracted neck injury metrics (Nij, Nkm, and Lateral Nij) were used to train Kriging surrogate models. These models produced clear response trends indicating that increased impact velocity and locational proximity to the driver often resulted in the greatest risk of inducing neck injury. Further, the impact angle variable typically produced the greatest risk under direct or slightly oblique angles regardless of the impact location or whether the impact was directed toward the occupant. This lack of interaction between the angle and location variables was likely caused by limitations within the injury metrics, themselves, which do not account for multi-axial or oblique loading, highlighting the need for improved metrics. Finally, distinct pairings of sub-metric component responses were noted in most impact scenarios. These trends may be a signifier for the primary modality of injury and should be assessed in a future study. [ABSTRACT FROM AUTHOR]

The study aims the effect of finite lip thickness and bypass ratio on subsonic and correctly expanded sonic co-flowing jet. The co-flowing jets characteristics were studied for two different lip thicknesses at subsonic Mach 0.6, 0.8, and sonic Mach 1.0 by varying the bypass ratio also the co-flowing jet area. The lip thickness considered for the study case is 1.0Dp and 1.5Dp (Dp – primary nozzle diameter is 10 mm). For experimental setup, the co-flowing duct area was varied the secondary inlet with 4 mm and 5 mm holes. Axial Pitot static tube survey was conducted experimentally. The numerical simulations were also carried by commercial code FLUENT- 6.3.2 for solving the RANS equations using Spalart–Allmaras turbulence model. The flow field has been visualised using numerical contours. The results indicate that for lip thickness 1.0Dp and for low bypass ratio, potential core seems to be thicker. Similar behaviour is observed in 1.5Dp lip thickness. On the other side, for both the lip thickness, 1.0Dp and1.5Dp, as the bypass ratio increases a recirculation zone occurs in the near field region and it becomes dominant. For bypass ratio 6.4 and 1.0Dp lip thickness, the recirculation zone exhibits an outer and an inner vortex. [ABSTRACT FROM AUTHOR]

Finite mixture models are useful for modeling lifetimes distribution of random samples arising from heterogeneous populations. In this work, we establish some stochastic comparison results for two finite mixtures models with components having generalized Lehmann distribution. [ABSTRACT FROM AUTHOR]

Let G be a finite non-abelian p-group of order greater than p4, p an odd prime, such that Z (Ω 1 (H)) is cyclic and Z(H) is elementary abelian, where H = C G (Φ (G)). We prove that the set A (G) = { α ∈ Aut (G) | [ x , α (x) ] = 1 for all x ∈ G } of all commuting automorphisms of G forms a subgroup of Aut (G) if and only if Ω 1 (H) is abelian. Also, we find the structure of A (G) = Aut z (G) for a finite 2-group G of almost maximal class with cyclic center Z(G), where Aut z (G) denotes the set of all central automorphisms of G. [ABSTRACT FROM AUTHOR]

In this article, we classify some finite p-groups whose normal subgroups are characteristic. Particularly we restrict our attention to all finite p-groups of maximal class with an abelian maximal subgroup, finite 3-groups of maximal class, finite split metacyclic p-groups, minimal non-abelian p-groups and all p-groups of maximal class of order less than p6. [ABSTRACT FROM AUTHOR]

Parsimonious finite mixture models often require the a priori selection of desired model dimensionality. For example, projection-based parsimonious models demand the dimension of the subspace for projection. Other models ask for their own structural restrictions on parameters. The subspace clustering framework is a projection-based parsimonious model for various finite mixtures, including the Gaussian variant. The existing dimension selection methods for subspace clustering are ad-hoc or potentially computationally prohibitive, creating a need for a principled, yet computationally lightweight, approach. In light of this problem, a hypothesis test-based intrinsic dimension estimation method called the Anderson Relaxation Test (ART) is introduced, and its performance is examined in both simulated and real data settings. [ABSTRACT FROM AUTHOR]

The present paper provides a procedure for constructing full-spark Parseval frames arising from the linear action of a 1-parameter group acting in R n . Precisely, given a square matrix A of order n, with real entries, we say that A induces the full spark frame property if the following conditions hold. There exists a vector v for which given any finite set X ⊂ R of cardinality n, the collection { exp ⁡ (x A) v : x ∈ X } is a basis for R n . First, we show that if the spectrum of A is not a subset of the reals, then A does not induce the full spark frame property. Secondly, we establish that if the spectrum of A is a subset of the reals, then A induces the full spark frame property if and only if every eigenvalue of A has geometric multiplicity one. The proof of the latter fact gives a new algorithm for the construction of a class of full spark Parseval frames for R n . [ABSTRACT FROM AUTHOR]

We propose exact exogeneity tests and weak-instruments-robust tests on factor loadings for a system of regressions with possibly non-Gaussian disturbances. Our methodology is valid in finite samples and accounts for common cross-sectional factors. Analytical invariance results are derived, with companion simulation studies. Finally, a total-effect parameter is introduced that embeds the unobservable endogeneity factor. Proposed tests are applied to assess whether Catastrophe bond mutual funds co-move with financial markets. Significant risk premiums are detected globally and over time, although they are less pervasive from a domestic currency perspective. Findings underscore the importance of instrumenting and assessing direct and total effects. [ABSTRACT FROM AUTHOR]

Best linear unbiased estimators (BLUE's) are known to be optimal in many respects under normal assumptions. Since variance minimization doesn't depend on normality and unbiasedness is often considered reasonable, many statisticians have felt that BLUE's ought to preform relatively well in some generality. The result here considers the general linear model and shows that any measurable estimator that is unbiased over a moderately large family of distributions must be linear. Thus, imposing unbiasedness cannot offer any improvement over imposing linearity. The problem was suggested by Hansen, who showed that any estimator unbiased for nearly all error distributions (with finite covariance) must have a variance no smaller than that of the best linear estimator in some parametric subfamily. Specifically, the hypothesis of linearity can be dropped from the classical Gauss–Markov Theorem. This might suggest that the best unbiased estimator should provide superior performance, but the result here shows that the best unbiased regression estimator can be no better than the best linear estimator. [ABSTRACT FROM AUTHOR]

Finite cotangent sums are closely related to values of the Riemann zeta function at the positive even integers. Over the past decades, numerous authors have obtained explicit evaluations of these sums. In this note, we present an intuitive evaluation using Laurent coefficients of powers of the cotangent function. In fact, our expression is a concise restatement of a well-known formula by Berndt and Yeap that was obtained using contour integration. [ABSTRACT FROM AUTHOR]