Semidefinite Research Articles

Lifting problem for universal quadratic forms over totally real cubic number fields

AbstractLifting problem for universal quadratic forms asks for totally real number fields that admit a positive definite quadratic form with coefficients in that is universal over the ring of integers of . In this paper, we show is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.

Morphological variability of verbs in the methodological and aplicational contexts

Abstract The goal of our contribution is to find an adequate methodological platform for describing and explaining the so-called inter-paradigmatic transition of Slovak verbs from the conjugation prototype česať (“to comb”, 1483 lexemes) to the conjugation prototype chytať (“to catch”). This transition is not linear and smooth. We understand the description of the given phenomenon as the construction of a linguistic model – a “transition scheme” – based on systemic linguistics (specifically, functional and structural linguistics). This platform, with the concepts of function, norm, system, center, and periphery, is compatible with the cognitive concepts of prototype and continuum, which we include in the construction of the model as certain components of the user and practical dimensions. From the point of view of formal morphology, we rely most on the description system of Slovak conjugation by M. Sokolová (2019). We drew material from the Orthographic and Grammatical Dictionary and verified the occurrence of variants on the set of corpora Omnia Slovaca IV consisting of the Slovak National Corpus, specialized corpora and web corpora. We conclude that the goal of the analyzed cross-paradigmatic movement is not the transition of verbs from the prototype česať to the prototype chytať, but rather the optimal balance of definite and indefinite forms of each verb with regard to the defined conjugation prototype under the simultaneous interaction of pragmatic, frequency and phonological factors.

Analisis Kesalahan Siswa dalam Menyelesaikan Soal Integral Bentuk Tak Tentu

In this research, researchers analyzed students' errors in solving questions on the topic of indefinite form integrals. The purpose of this research is to determine the patterns of student errors that often occur when working on indefinite form integral questions, as well as the factors that cause them. The subjects in this research were 25 grade 11 high school students. This research was carried out by providing a test sheet in the form of essay questions on the subject matter of indefinite integrals, totaling 5 questions with 1 category of easy questions, 3 categories of medium questions, and 1 category of difficult questions. Based on the results of data analysis, it was obtained that for question number 1 (an easy category question), 100% of respondents answered correctly. Question number 2 (medium category question), 93.3% of respondents answered correctly. Question number 3 (medium category question) 54% of respondents answered correctly. Question number 4 (difficult category question), 46% of respondents answered correctly. Meanwhile, for question number 5 (difficult category question), only 20% of respondents answered correctly.

A Passivity-based Control Combined with Sliding Mode Control for a DC-DC Boost Power Converter

In this paper, a passivity-based control combined with sliding mode control for a DC-DC boost power converter is proposed. Moreover, a passivity-based control for a DC-DC boost power converter is also proposed. Using a co-ordinate transformation of state variables and control input, a DC-DC boost power converter is passive. A new plant is zero-state observable and the equilibrium point at origin of this plant is asymptotically stable. Then, a passivity-based control is applied to this plant such that the capacitor voltage is equal to the desired voltage. Additionally, the sliding mode control law is chosen such that the derivative of Lyapunov function is negative semidefinite. Finally, a passivity-based control combined with sliding mode control law is applied to this plant such that the capacitor voltage is equal to the desired voltage. The simulation results of the passivity-based control, the sliding mode control and the passivity-based control combined with sliding mode control demonstrate the effectiveness and show that the capacitor voltage is kept at the desired voltage when the desired voltage, the input voltage E and the load resistor R are changed. The results show that compared with the passivity-based control, the passivity-based control combined with sliding mode control has better performance such as shorter settling time, 8.5 ms when R changes and it has smaller steady-state error, which is indicated by the value of integral absolute error (IAE), 0.0679 when the desired voltage changes. The paper has limitations such as the assumed circuit parameters.

Особенности глагольных фразеологизмов в ингушском языке

The aim of the research is to identify the characteristics of verbal phraseological units in the Ingush language. Ingush phraseological units that include a verb as a core component exhibit a diverse composition. The analysis of groups of verbal phraseological units in the study made it possible to characterize their structural features. The scientific novelty of the work lies in defining the structural and semantic characteristics of verbal phraseological units in the Ingush language. As a result of the research, verbal phraseological units in the Ingush language have been identified and systematized and their structural patterns have been determined. It has been proved that the composition of verbal phraseological units in the Ingush language is extremely diverse in terms of the structure and the meaning of the components involved. It is noted that in verbal phraseological units, transitive and intransitive verbs in the indefinite form are commonly used as the core component. Verbal phraseological units in the Ingush language are predominantly two-component. It has been determined that in the Ingush language, the majority of phraseological units with a verb as the core component, while possessing a qualitatively new meaning, maintain a strong connection with free word combinations.

Moduli of polarised Enriques surfaces — Computational aspects

AbstractModuli spaces of (polarised) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to isomorphism, only finitely many different moduli spaces of polarised Enriques surfaces. Here, we investigate the possible arithmetic groups and show that there are exactly 87 such groups up to conjugacy. We also show that all moduli spaces are dominated by a moduli space of polarised Enriques surfaces of degree 1240. Ciliberto, Dedieu, Galati and Knutsen have also investigated moduli spaces of polarised Enriques surfaces in detail. We discuss how our enumeration relates to theirs. We further compute the Tits building of the groups in question. Our computation is based on groups and indefinite quadratic forms and the algorithms used are explained.

SAT483 Role of Cholestyramine in Refractory Amiodarone-induced Thyrotoxicosis

Abstract Disclosure: H. Zhao: None. J. Leung: None. Role of Cholestyramine in Refractory Amiodarone-Induced Thyrotoxicosis. Background: Amiodarone-induced thyrotoxicosis (AIT) is divided into type 1 (AIT1; treated with thioamides) and type 2 (AIT2; treated with glucocorticoids). Combined therapy is utilized in mixed or indefinite forms. When medical treatment is unsuccessful, radioiodine ablation or thyroidectomy are considered. Clinical Case: A 76-year-old gentleman, with a history of atrial fibrillation treated with amiodarone, presented with recurrent atrial fibrillation refractory to cardioversion. Investigations revealed TSH <0.01, FT4 58.1 (ref 10.0-20.0 pmol/L), FT3 16.0 (ref 3.5-6.5 pmol/L), TPO negative and TRAB negative. As thyroid ultrasound revealed absence of focal nodules or hypervascularity and technetium pertechnetate scan demonstrated no thyroid activity, AIT2 was suspected. Prednisone was initiated and amiodarone discontinued. Due to minimal response after a month, a mixed type was suggested and methimazole added. Despite intensification of the antithyroid regimen, FT4 increased to 59.5. Methimazole was discontinued for radioiodine ablation assessment. Given low thyroid uptake (<3%), ablation was deemed unlikely beneficial. After patient refused thyroidectomy, cholestyramine was initiated, resulting in significant improvement, with FT4 declining from 46.0 to 29.0 in 2 weeks. Euthyroidism was achieved after 2 months of cholestyramine treatment and medications were stopped. At 6 months post presentation, he developed amiodarone-related hypothyroidism and began levothyroxine. Conclusion: Previous reports propose that cholestyramine, an ion exchange resin, interrupts enterohepatic circulation of thyroid hormone and demonstrated the use of cholestyramine in refractory Grave’s hyperthyroidism. This is one of the first few reports demonstrating the possible role of cholestyramine in AIT refractory to first line medical therapy. Presentation Date: Saturday, June 17, 2023

Fixed/preassigned-time output synchronization for T–S fuzzy complex networks via quantized control

This article is devoted to the analysis of fixed-time (FXT) and preassigned-time (PAT) output synchronization for T–S fuzzy complex networks (CNs). Firstly, to improve transmission efficiency of information, a kind of pure power-law control strategy with logarithmic quantization is designed and the power-law terms have only one free parameter. Then, by applying FXT stability theorem as well as inequality skills, some compact criteria are obtained to achieve FXT output synchronization of T–S fuzzy CNs, and the restriction on the output matrix with positive definite and diagonal form is removed. Furthermore, the PAT output synchronization of T–S fuzzy CNs is further explored by developing a quantized control scheme with power-law form. Three numerical examples in the end are given to attest the proposed control design and criteria.

Modulus Constrained Minimax Radar Code Design Against Target Interpulse Fluctuation

In the presence of colored Gaussian disturbance, this paper considers the robust transmit code and receiver filter design against target interpulse fluctuation while guaranteeing the dynamic range and energy of the transmit code. Aiming at enhancing the worst-case Signal-to-Noise-Ratio (SNR) over a spherical set, the design is cast as a non-convex minimax problem. It is shown that the filter can be directly derived based on the strong max-min property of the objective function. Then, the semi-definite relaxation form of the resultant problem is proved to be hidden convex by exploiting the strong duality of the Quadratically-Constrained Quadratic Programming (QCQP) problem. Finally, the robust code-filter pair can be effectively synthesized based on a randomization scheme. At the analysis stage, numerical results are shown to highlight the superiority of the proposed design.

Can we recover an integral quadratic form by representing all its subforms?

Let o be the ring of integers of a number field. If f is a quadratic form over o and g is another quadratic form over o which represents all proper subforms of f, does g represent f? We show that if g is indefinite, then g indeed represents f. However, when f is positive definite and indecomposable, then there exists a g which represents all proper subforms of f but not f itself. Along the way we give a new characterization of positive definite decomposable quadratic forms over o and a number-field generalization of the finiteness theorem of representations of quadratic forms by quadratic forms over Z[13, Theorem 3.3] which asserts that given any infinite set S of classes of positive definite integral quadratic forms over o of a fixed rank, there exists a finite subset S0 of S with the property that a positive definite quadratic form over o represents all classes in S if and only if it represents all classes in S0.

On average theta functions of certain quadratic forms as sums of Eisenstein series

Abstract Let Q Q be an integral positive definite quadratic form of level N N in 2 k 2k variables. Further, we assume that ( − 1 ) k N {\left(-1)}^{k}N is a fundamental discriminant. We express the average theta function of Q Q as an explicit sum of Eisenstein series, which are Hecke eigenforms by applying Atkin-Lehner involution.

Second moment of the light-cone Siegel transform and applications

We study the light-cone Siegel transform, transforming functions on the light cone of a rational indefinite quadratic form Q to a function on the homogenous space SOQ+(Z)﹨SOQ+(R). In particular, we prove a second moment formula for this transform for forms of signature (n+1,1), and show how it can be used for various applications involving counting integer points on the light cone. In particular, we prove some new results on intrinsic Diophantine approximations on ellipsoids as well as on the distribution of values of random linear and quadratic forms on the light cone.

Optimized Statistical Beamforming for Cooperative Spectrum Sensing in Cognitive Radio Networks

In cognitive radio (CR), cooperative spectrum sensing (CSS) employs a fusion of multiple decisions from various secondary user (SU) nodes at a central fusion center (FC) to detect spectral holes not utilized by the primary user (PU). The energy detector (ED) is a well-established technique of spectrum sensing (SS). However, a major challenge in designing an energy detector-based SS is the requirement of correct knowledge for the distribution of decision statistics. Usually, the Gaussian assumption is employed for the received statistics, which is not true in real practice, particularly with a limited number of samples. Another big challenge in the CSS task is choosing an optimal fusion strategy. To tackle these issues, we have proposed a beamforming-assisted ED with a heuristic-optimized CSS technique that utilizes a more accurate distribution of decision statistics by employing the characterization of the indefinite quadratic form (IQF). Two heuristic algorithms, genetic algorithm with multi-parent crossover (GA-MPC) and constriction factor particle swarm-based optimization (CF-PSO), are developed to design optimum beamforming and optimum fusion weights that can maximize the global probability of detection pd while constraining the global probability of false alarm pf to below a required level. The simulation results are presented to validate the theoretical findings and to asses the performance of the proposed algorithm.

An online generalized multiscale approximation of the multipoint flux mixed finite element method

In this paper, we develop an online generalized multiscale approximation of the multipoint flux mixed finite element method (MFMFE) for Darcy flow in highly heterogeneous porous media, which can handle full tensor permeability fields and unstructured grids with local velocity elimination. Here, for illustration of the proposed method, we will mainly consider the situation that the porous medium is filled with fractures, which usually results in unstructured grids, and the extension to the situation that the permeability is represented as a full tensor is straightforward. From the fine-grid discretization by the MFMFE method, we derive the symmetric and positive definite discrete bilinear form for both the matrix and fracture pressure, and thereby obtain the corresponding discrete weak formulation that only related to pressure. In the offline stage, we compute offline basis functions which contain the important local multiscale information of each coarse-grid block to form the initial multiscale space. In the online stage, we construct and add online basis functions to enrich the multiscale space and consequently improve the accuracy of the multiscale solution. Each offline basis function and each online basis function contains multiscale information both for matrix and fracture. We give the theoretical analysis for the convergence of the online enrichment, which shows that more sufficient initial basis functions lead to faster convergence rates. A series of numerical examples that either the permeability is a full tensor or the porous medium is filled with fractures are presented to show the performance of the multiscale method.

Isolations of cubic lattices from their proper sublattices

A (positive definite and integral) quadratic form is called an isolation of a quadratic form f if it represents all subforms of f except for f itself. The minimum rank of isolations of a quadratic form f is denoted, if it exists, by Iso(f). In this article, we show that Iso(I2)=5 and Iso(I3)=6, where In=x12+…+xn2 is the sum of n squares for any positive integer n. After proving that there always exists an isolation of In for any positive integer n, we provide some explicit lower and upper bounds for Iso(In). In particular, we show that Iso(In)∈Ω(n32−ϵ) for any ϵ>0.

A new theorem on finite‐time stability of stochastic homogeneous systems and its application

AbstractThis paper provides a novel Lyapunov theorem on finite‐time stability of stochastic homogeneous systems. Different from the existing results, the differential operator in this paper is not required to be negative definite and could be negative semidefinite. The obtained condition is somehow similar to the LaSalle's condition. Moreover, the existing theorem of finite‐time stability for stochastic homogeneous systems is a special case of our result. As an application of the obtained theorem, stochastic finite‐time stabilization is considered for stochastic homogeneous affine control systems. Some examples and simulations are provided to show the effectiveness of the results.

Performance analysis of NOMA enabled multi-user co-operative IoT network with SWIPT protocol

This study investigates the performance of user equipments (UEs) and IoT devices in a multi-user (MU) multiple-input single-output (MISO) configuration based non-orthogonal multiple-access (NOMA) system. The proposed model includes a base station surrounded by many users and a number of dispersed IoT devices. In the considered MU IoT network scenario, power allocation coefficients are set to ensure that both the relaying UE and the targeted IoT device experience increased performance. To assist the intended IoT device with weak channel conditions, an optimal user selection method is developed that picks a UE with comparatively better reception, and thereby the selected UE acts as relay forward node utilizing the simultaneous wireless information and power transfer protocol. The characterization of a key performance metric, i.e., the outage probability is derived by adopting a two-step procedure. First, quadratic forms of signal to interference plus noise ratio (SINR) at the relaying UE and the signal-to-noise ratio (SNR) and SINR at the intended IoT device are constructed. Then, using the indefinite quadratic form approach, we arrive at closed-form expressions for the outage probability (OP) of intended IoT device under linearly dependent beamformers. To validate the analytical expressions provided in this study, simulations are performed. We demonstrate that by utilizing the proposed user selection technique in MU-MISO-NOMA system decreases the OP of the intended IoT device by 40% on average. Furthermore, utilizing multiple transmit antenna elements decreases the OP of the intended IoT device by approximately 10%.

Sum of the Fourier coefficients of SL(3,Z) Hecke Maass forms over quadratics

Let A(1,n) denote the (1,n)-th Fourier coefficients of a SL(3,Z) Hecke eigenform. Let Q(x,y) be a symmetric positive definite quadratic form. In this paper, we shall prove thatS:=∑m≤X∑n≤XA(1,Q(m,n))W1(mX)W2(nX)≪X2−168+ϵ, for any positive ϵ>0, where W1 and W2 are smooth bump functions supported on the interval [1,2].

Modern forest climatopes and forest typological zoning of the northern part of European Russia

The article considers the current problem of modern scheme of Russia forest zoning designing and methods of forest typological assessment of forest climatopes and forest typological zoning. For the northern part of European Russia at the beginning of the XXI century, the climates of forest thermotopes, contrastotopes and hygrotopes, their spatial distribution, geographical stretching and zoning has been determined by classical forest typological methods. It has been ascertained four zones of forest climatopes, four zones of continentality (zones of forest contrastotopes), one of that has separate semienclave from the White and Barents Seas, and five zones of forest hygrotopes (one of that is disjunctive). A new, previously undescribed climate of the contrastotop of the mild (seaside) forest climate has been identified, requiring an assessment of the forest-growing effect. It has been established that the modern zones of forest thermo-, contrast- and hygrotopes have a different nature of geographical extent, and modern boundaries of zones have characterized by dynamical mobility and indefinite form in most cases, especially boundaries of forest hygrotopes climate zones. The modern forest typological zoning of the northern part of European Russia is proposed according to three equivalent climatic regimes and it has established forest typological regions with maximal area. In connection with complicate of boundaries of zones character it is established that the greatest diversity of forest typological areas are between boundaries of thermotopes and hygrotopes climate zones and from White and Barents Seas and Ural Mountains. The question is raised about the assessment of the actual existence of some selected local forest typological areas as geographical ecotones.

КӨРКӨМ ЧЫГАРМАДАГЫ УБАКТЫЛУУ-КӨРҮНҮШТҮК ФОРМАНЫН ЖАРАЛУУ ПРИНЦИПТЕРИ

Time, type, and temporal displacement are the meanings of forms of microsystems that differ from each other. Artistic time subjugates grammatical time: the present time form is not expressed as "present, now" to any author's speech, nor to any recipient. Here, authorial and reader time, on the one hand, are opposed to the character time, and on the other hand, such a discrepancy is not necessary when using the past tense form. Such multiplicity of temporal- visual form is resolved according to the nature of the relationship, which penetrates and mixes with the highest-level unity of the artistic text. The meaning of the present indefinite form derives from the paradigmatic and syntagmatic core meaning. As soon as these forms are added to the text, their meaning is superimposed on the meaning that has passed. These meanings are not mutually exclusive, they are interrelated. The intersection of various meanings into one form plays a big role in the semantic organization of the temporal structure of the work of art. Having such a complex semantics of the temporal-visual form is a feature of the artistic text.