Decomposed Form Research Articles

Bounds for the solutions of $S$-unit equations and decomposable form equations II.

Bounds for the solutions of $S$-unit equations and decomposable form equations II.

Square-free Values of Decomposable Forms

AbstractIn this paper we prove that decomposable forms, or homogeneous polynomials F(x1, . . . , xn) with integer coefficients that split completely into linear factors over , take on infinitely many square-free values subject to simple necessary conditions, and they have deg f ≤ 2n + 2 for all irreducible factors f of F. This work generalizes a theorem of Greaves.

Compiling CP subproblems to MDDs and d-DNNFs

Modeling discrete optimization problems is not straightforward. It is often the case that precompiling a subproblem that involves only a few tightly constrained variables as a table constraint can improve solving time. Nevertheless, enumerating all the solutions of a subproblem into a table can be costly in time and space. In this work we propose using Multivalued Decision Diagrams (MDDs) and formulas in Deterministic Decomposable Negation Normal Form (d-DNNFs) rather than tables to compute and store all solutions of a subproblem. This, in turn, can be used to enhance the solver thanks to stronger propagation via specific propagators for these structures. We show how to precompile part of a problem into both these structures, which can then be injected back in the model by substituting the constraints it encodes, or simply adding it as a redundant constraint. Furthermore, in the case of MDDs, they can also be used to create edge-valued MDDs for optimization problems with an appropriate form. From our experiments we conclude that all three techniques are valuable in their own right, and show when each one should be chosen over the others.

Polyprograms and Polyprogram Bisimulation

A polyprogram is a generalization of a program which admits multiple definitions of a single function. Such objects arise in different transformation systems, such as the Burstall-Darlington framework or equality saturation. In this paper, we introduce the notion of a polyprogram in a non-strict first-order functional language. We define denotational semantics for polyprograms and describe some possible transformations of polyprograms, namely we present several main transformations in two different styles: in the style of the Burstall-Darlington framework and in the style of equality saturation. Transformations in the style of equality saturation are performed on polyprograms in decomposed form, where the difference between functions and expressions is blurred, and so is the difference between substitution and unfolding. Decomposed polyprograms are well suited for implementation and reasoning, although they are not very human-readable. We also introduce the notion of polyprogram bisimulation which enables a powerful transformation called merging by bisimulation, corresponding to proving equivalence of functions by induction or coinduction. Polyprogram bisimulation is a concept inspired by bisimulation of labelled transition systems, but yet it is quite different, because polyprogram bisimulation treats every definition as self-sufficient, that is a function is considered to be defined by any of its definitions, whereas in an LTS the behaviour of a state is defined by all transitions from this state. We present an algorithm for enumerating polyprogram bisimulations of a certain form. The algorithm consists of two phases: enumerating prebisimulations and converting them to proper bisimulations. This separation is required because polyprogram bisimulations take into account the possibility of parameter permutation. We prove correctness of this algorithm and formulate a certain weak form of its completeness. The article is published in the author’s wording.

Synthesis, Characterization and Catalytic Activity of Quadruple Perovskite: CaCu3‐xMnxTi4‐xMnxO12 (x=0, 0.5 and 1.0)

AbstractWe report the low temperature synthesis of nanosized CaCu3‐xMnxTi4‐xMnxO12 (x= 0, 0.5 and 1.0) quadruple perovskites and their magnetic, dielectric and catalytic performance towards CO oxidation and methanol steam reforming (MSR). Our investigations reveal the pronounced effects of particle size and chemical substitution on all the physical properties reported here. The manganese doped samples exhibit remarkable change in magnetic properties, where antiferromagnetic pristine phase converted to ferrimagnetic phase for x=1. The dielectric constant values of the cold‐pressed nanosized perovskites are ∼103 and follows Maxwell‐Wagner type relaxation. This value is about 100 fold lower than that of the bulk samples that has been ascribed to the effect of particle size and the absence of nano‐twinning in the material as revealed from HRTEM studies. The doping of manganese further reduces the magnitude of dielectric value, which is the chemical effect. Mn‐doped samples show greater catalytic activity compared to the pristine sample towards CO oxidation due to a synergistic Cu−Mn interaction. The catalytic performance of these oxides for MSR reaction is intriguing. Although the catalyst undergoes decomposition in the MSR atmosphere causing a decrease in methanol conversion during time‐on‐stream (TOS) tests, the activity can be regenerated by in‐situ or ex‐situ annealing in air. The notable catalytic activity and reversibility between pristine and decomposed form are very interesting.

$S$-parts of values of univariate polynomials,\\ binary forms and decomposable forms at integral points

Let $S = \{p_1, \ldots , p_s\}$ be a finite, non-empty set of distinct prime numbers. For a non-zero integer $m$, write $m = p_1^{a_1} \ldots p_s^{a_s} b$, where $a_1, \ldots , a_s$ are non-negative integers and $b$ is an integer relatively prime to

Computational Identification of Irreducible State-Spaces for Stochastic Reaction Networks

Stochastic models of reaction networks are becoming increasingly important in systems biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent species. The state-space on which this process resides is a subset of a nonnegative integer lattice, and for many examples of interest, this state-space is countably infinite. This causes numerous problems in analyzing the Markov chain and understanding its long-term behavior. These problems are further confounded by the presence of conservation relations among species which constrain the dynamics in complicated ways. In this paper we provide a linear-algebraic procedure to disentangle these conservation relations and represent the state-space in a special decomposed form, based on the copy-number ranges of various species and dependencies among them. This decomposed form is advantageous for analyzing the stochastic model, and for a large class of networks we demonstrate how this form can be used for finding all the closed communication classes for the Markov chain within the infinite state-space. Such communication classes are irreducible state-spaces for the dynamics and they support all the extremal stationary distributions for the Markov chain. Hence our results provide important insights into the long-term behavior and stability properties of stochastic models of reaction networks. We discuss how the knowledge of these irreducible state-spaces can be used in many ways such as speeding-up stochastic simulations of multiscale networks or in identifying the stationary distributions of complex-balanced networks. We illustrate our results with several examples of gene-expression networks from systems biology.

A structural model updating method using incompletepower spectral density function and modal data

In this study, a frequency domain model updating method is presented using power spectral density (PSD) data. It uses the sensitivity of PSD function with respect to the unknown structural parameters through a decomposed form of transfer function. The stiffness parameters are captured with high accuracy through solving the sensitivity equations utilizing the least square approach. Using numerically noise polluted data, the model updating results of a truss model prove robustness of the method against measurement and mass modelling errors. Results prove the capabilities of the method for parameter estimation using highly noise polluted data of low ranges of excitation frequency.

Kato–Milne cohomology and polynomial forms

Given a prime number p, a field F with char(F)=p and a positive integer n, we study the class-preserving modifications of Kato–Milne classes of decomposable differential forms. These modifications demonstrate a natural connection between differential forms and p-regular forms. A p-regular form is defined to be a homogeneous polynomial form of degree p for which there is no nonzero point where all the order p−1 partial derivatives vanish simultaneously. We define a C˜p,m field to be a field over which every p-regular form of dimension greater than pm is isotropic. The main results are that for a C˜p,m field F, the symbol length of Hp2(F) is bounded from above by pm−1−1 and for any n⩾⌈(m−1)log2⁡(p)⌉+1, Hpn+1(F)=0.

Vortex force map method for viscous flows of general airfoils

In a previous paper, an inviscid vortex force map approach was developed for the normal force of a flat plate at arbitrarily high angle of attack and leading/trailing edge force-producing critical regions were identified. In this paper, this vortex force map approach is extended to viscous flows and general airfoils, for both lift and drag forces due to vortices. The vortex force factors for the vortex force map are obtained here by using Howe’s integral force formula. A decomposed form of the force formula, ensuring vortices far away from the body have negligible effect on the force, is also derived. Using Joukowsky and NACA0012 airfoils for illustration, it is found that the vortex force map for general airfoils is similar to that of a flat plate, meaning that force-producing critical regions similar to those of a flat plate also exist for more general airfoils and for viscous flow. The vortex force approach is validated against NACA0012 at several angles of attack and Reynolds numbers, by using computational fluid dynamics.

Normalization in Riemann Tensor Polynomial Ring

It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grobner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grobner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grobner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grobner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.

Morgan’s problem of Boolean control networks

This paper investigates the Morgan’s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an outputdecomposed form by constructing a set of consistent output-friendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan’s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan’s problem is obtained.

Artificial noise-aided biobjective transmitter optimization for service integration in multi-user MIMO broadcast channel

This paper considers an artificial noise (AN)-aided transmit design for multi-user MIMO systems with integrated services. Specifically, two sorts of service messages are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver and required to be perfectly secure from other unauthorized receivers. Our interest lies in the joint design of input covariances of the multicast message, confidential message, and artificial noise (AN), such that the achievable secrecy rate and multicast rate are simultaneously maximized. This problem is identified as a secrecy rate region maximization (SRRM) problem in the context of physical-layer service integration. Since this biobjective optimization problem is inherently complex to solve, we put forward two different scalarization methods to convert it into a scalar optimization problem. First, we propose to prefix the multicast rate as a constant, and accordingly, the primal biobjective problem is converted into a secrecy rate maximization (SRM) problem with quality of multicast service (QoMS) constraint. By varying the constant, we can obtain different Pareto optimal points. The resulting SRM problem can be iteratively solved via a provably convergent difference-of-concave (DC) algorithm. In the second method, we aim to maximize the weighted sum of the secrecy rate and the multicast rate. Through varying the weighted vector, one can also obtain different Pareto optimal points. We show that this weighted sum rate maximization (WSRM) problem can be recast into a primal decomposable form, which is amenable to alternating optimization (AO). Then, we compare these two scalarization methods in terms of their overall performance and computational complexity via theoretical analysis as well as numerical simulation, based on which new insights can be drawn.

The influence of the morphological structure of words on the dynamics of handwriting in adults and fourth and sixth grade children

Grapheme and syllable units have been shown to influence the dynamics of handwriting in adults and children, but the influence of morphemes remains to be clarified. We tested the ability of French-speaking adults and fourth and sixth grade children to process the morphological structure of words during writing. They were asked to copy three types of words on a digitizer: morphologically complex words, morphologically simple words matched for the bigram at the syllabic boundary, and morphologically simple words matched for the bigram at the morphemic boundary. Latencies were shorter for morphologically complex words than for simple words only in adults. Requiring individuals to process morphological structure increased the time taken to write the letter before a morphemic boundary in adults and sixth graders. In contrast, fourth graders wrote the letter before the syllabic boundary more quickly for complex words than for simple words. These results indicate that words are represented in a decomposed form in the lexicon, and that the morphological structure of words regulates the dynamics of handwriting.

Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime

The electromagnetic field correlators are evaluated around a cosmic string in background of (D+1)-dimensional dS spacetime assuming that the field is prepared in the Bunch–Davies vacuum state. The correlators are presented in the decomposed form where the string-induced topological parts are explicitly extracted. With this decomposition, the renormalization of the local vacuum expectation values (VEVs) in the coincidence limit is reduced to the one for dS spacetime in the absence of the cosmic string. The VEVs of the squared electric and magnetic fields, and of the vacuum energy density are investigated. Near the string they are dominated by the topological contributions and the effects induced by the background gravitational field are small. In this region, the leading terms in the topological contributions are obtained from the corresponding VEVs for a string on the Minkowski bulk multiplying by the conformal factor. At distances from the string larger than the curvature radius of the background geometry, the pure dS parts in the VEVs dominate. In this region, for spatial dimensions D>3, the influence of the gravitational field on the topological contributions is crucial and the corresponding behavior is essentially different from that for a cosmic string on the Minkowski bulk. There are well-motivated inflationary models which produce cosmic strings. We argue that, as a consequence of the quantum-to-classical transition of super-Hubble electromagnetic fluctuations during inflation, in the post-inflationary era these strings will be surrounded by large-scale stochastic magnetic fields. These fields could be among the distinctive features of the cosmic strings produced during the inflation and also of the corresponding inflationary models.

Identification of milling process damping using operational modal analysis

Abstract This paper provides a novel approach for identifying the process damping directly from chatter-free milling tests. First, power spectrum density matrix of cutter's deflections is theoretically derived by introducing transfer function and random excitation force, and the spectral decomposition of the power spectrum density matrix is formulated as an explicit function of modal parameters. Then, exponential attenuation method is adopted to extract the damping ratios from the inverse Fourier transformation result of the decomposed form. Finally, tangential and radial ploughing force coefficients, which are utilized to characterize process damping, are simultaneously calculated based on energy balance principle. Besides, experimental setup consisting of displacement sensors is specially designed to measure the cutter's deflections, which are further used to calculate the power spectrum density required in the above identification procedure. It is experimentally proven that the accuracy of chatter stability limits in milling process is improved when the proposed process damping model is considered.

Release of Phosphorus Forms from Cover Crop Residues in Agroecological No-Till Onion Production

Cover crops grown alone or in association can take up different amounts of phosphorus (P) from the soil and accumulate it in different P-forms in plant tissue. Cover crop residues with a higher content of readily decomposed forms may release P more quickly for the next onion crop. The aim of this study was to evaluate the release of P forms from residues of single and mixed cover crops in agroecological no-till onion (Allium cepa L.) production. The experiment was conducted in Ituporanga, Santa Catarina (SC), Brazil, in an Inceptisol, with the following treatments: weeds, black oat (Avena sativa L.), rye (Secale cereale L.), oilseed radish (Raphanus sativus L.), oilseed radish + black oat, and oilseed radish + rye. Cover crops were sown in April 2013. In July 2013, plant shoots were cut close to the soil surface and part of the material was placed in litterbags. The bags were placed on the soil surface and residues were collected at 0, 15, and 45 days after deposition (DAD). Residues were dried and ground and P in the plant tissue was determined through chemical fractionation. The release of P contained in the tissue of cover crops depends not only on total P content in the tissue, but also on the accumulation of P forms and the quality of the residue in decomposition. The highest accumulation of P in cover crops occurred in the soluble inorganic P fraction, which is the fraction of fastest release in plants. Black oat had the highest initial release rate of soluble inorganic P, which became equal to the release rate of other cover crop residues at 45 DAD. Weeds released only half the amount of soluble inorganic P in the same period, despite accumulating a considerable amount of P in their biomass. The mixtures of oilseed radish + rye and oilseed radish + black oat showed higher release of P associated with RNA at 45 DAD in comparison to the single treatments.

Movement of time-delayed hot spots in Euclidean space

We investigate the shape of the solution of the Cauchy problem for the damped wave equation. In particular, we study the existence, location and number of spatial maximizers of the solution. Studying the shape of the solution of the damped wave equation, we prepare a decomposed form of the solution into the heat part and the wave part. Moreover, as its another application, we give $L^p$-$L^q$ estimates of the solution.

Meta-Symplectic Geometry of 3rdOrder Monge-Ampère Equations and their Characteristics

This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Amp\`ere equations, by using the so-called "meta-symplectic structure" associated with the 8D prolongation $M^{(1)}$ of a 5D contact manifold $M$. We write down a geometric definition of a third-order Monge-Amp\`ere equation in terms of a (class of) differential two-form on $M^{(1)}$. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Amp\`ere equations, herewith called of Goursat type.

Regional CO2 solubility trapping potential of a deep saline aquifer in Pohang basin, Korea

This paper presents regional CO2 solubility trapping potential for stable CO2 storage as immobile phase and decomposed form while CO2 migrates through flow pathways characterized by the geological structure of an aquifer in Pohang basin, SE offshore Korea. The saline aquifer in Pohang basin has been selected as a target formation for geologic carbon storage due to favorable geologic structures and sedimentary strata defined through seismic survey. The aquifer is confined by southeast and northwest faults, and structure is unconfined and sloping toward the northeast direction. The main target within the aquifer to store CO2 contains west plunging anticlines. In order to enlarge contact area of CO2 with brine and improve injectivity, the CO2 injector is located on marginal anticlines or small synclines. This structure may significantly affect CO2 flow dynamics through upward migration pathways within the aquifer. We, in this area, provide estimates for CO2 solubility trapping affected by dynamic CO2 migration pathways and present different types of CO2 trapping potentials. The numerical results based on thermodynamic equilibrium equation provide regional CO2 solubility trapping potential which has a linear relationship with brine salinity. We suggest that dynamic migration pathways resulting from geological structure are significantly important to increase CO2 solubility trapping potential in geological storage of CO2.