Search

Modular Multilevel Converters (MMC) have found extensive application in connecting Renewable Energy Sources to the power grid. Recently, MMCs operated in the Grid Forming (GFM) mode have garnered significant interest due to their superior performance in weak AC networks. The Virtual Synchronous Generator (VSG) is a GFM technology designed to emulate the behavior of a real synchronous generator (SG). There is flexibility in selecting the VSG's parameters as they are not constrained by the physical attributes of an actual SG. This paper proposes employing the Genetic Algorithm (GA) to select these parameters, underscoring its simplicity and effectiveness in meeting diverse constraints and objectives. Small Signal (SS) models are constructed at potential operational points, with GA leveraging the SS model's eigenvalues to select parameter values that enhance dynamic performance, ensuring resilience across a wide range of operating conditions. The effectiveness of these designed parameters is validated through Electromagnetic Transients (EMT) simulations. • A novel virtual synchronous generator (VSG) controller with parameter flexibility. • VSG damping optimization through Genetic Algorithms (GA) ensuring stability. • VSG robust optimization for multiple operating points via GA. [ABSTRACT FROM AUTHOR]

The cohomology theory TMF of topological modular forms is a derived algebro-geometric interpretation of the ring of complex modular forms from number theory. In this article, we refine the classical Adams operations, Hecke operators, and Atkin–Lehner involutions from endomorphisms of modular forms to stable operators on TMF. Our algebro-geometric formulation of these operators leads to simple proofs of their many remarkable properties and computations. From these properties, we use techniques from homotopy theory to make simple number-theoretic deductions, including a rederivation of some classical congruences of Ramanujan and providing new infinite families of Hecke operators which satisfy Maeda's conjecture. [ABSTRACT FROM AUTHOR]

The ghost conjecture is first provided by Bergdall and Pollack in [1,2] to study the U p -slopes of spaces of modular forms, which, so far, has already brought plenty of important results. The local version of this conjecture under genericity condition has been solved by Liu-Truong-Xiao-Zhao in [10,11]. In the current paper, we prove a necessary and sufficient condition for a sequence of local ghost series to satisfy that their product has the same Newton polygon to the ghost series build from the direct sum of their associated modules (see Theorem 1.2). That answers a common question asked in both [2,10]. [ABSTRACT FROM AUTHOR]

This paper studies the folding of square, kirigami-inspired space structures consisting of concentrically arranged modular elements formed by thin shells. Localized elastic folds are introduced in the thin shells and different folding strategies can be obtained by varying the location of the folds and the sequence of imposed rotations. Modeling each modular element with rigid rods connected by revolute joints, numerical simulations of the kinematics of folding are obtained, including constraints that represent folding aids and a gravity offload system. These simulations are used to study two specific packaging schemes, and the folding envelopes of a specific structure are analyzed to identify the scheme that is easier to implement in practice. This particular scheme is demonstrated by means of a physical prototype. • We study the folding of space structures consisting of concentric modular elements. • Different packaging schemes are obtained by varying the locations of localized elastic folds. • A numerical model, based on rigid rods with revolute joints, is used to simulate the folding kinematics. • Specific packaging schemes that can be achieved with simple folding aids and gravity offloads are studied. • The scheme that is easier to implement is selected for an experimental demonstration. [ABSTRACT FROM AUTHOR]

Let r ≥ 1 be a positive integer, A a real positive definite symmetric r × r rational matrix, B a rational vector of length r , and C a rational scalar. Nahm's problem is to find all triples (A , B , C) such that the r -fold q -hypergeometric series f A , B , C (q) : = ∑ n = (n 1 , ... , n r) T ∈ (Z ≥ 0) r q 1 2 n T A n + n T B + C (q ; q) n 1 ⋯ (q ; q) n r becomes a modular form, and we call such (A , B , C) a modular triple. When the rank r = 3 , after extensive computer searches, Zagier provided twelve sets of conjectural modular triples and proved three of them. We prove a number of Rogers–Ramanujan type identities involving triple sums. These identities give modular form representations for and thereby verify all of Zagier's rank three examples. In particular, we prove a conjectural identity of Zagier. [ABSTRACT FROM AUTHOR]

Background: Reliable, time- and cost-effective, and clinician-friendly diagnostic tools are cornerstones in facial palsy (FP) patient management. Different automated FP grading systems have been developed but revealed persisting downsides such as insufficient accuracy and cost-intensive hardware. We aimed to overcome these barriers and programmed an automated grading system for FP patients utilizing the House and Brackmann scale (HBS). Methods: Image datasets of 86 patients seen at the Department of Plastic, Hand, and Reconstructive Surgery at the University Hospital Regensburg, Germany, between June 2017 and May 2021, were used to train the neural network and evaluate its accuracy. Nine facial poses per patient were analyzed by the algorithm. Results: The algorithm showed an accuracy of 100%. Oversampling did not result in altered outcomes, while the direct form displayed superior accuracy levels when compared to the modular classification form (n = 86; 100% vs. 99%). The Early Fusion technique was linked to improved accuracy outcomes in comparison to the Late Fusion and sequential method (n = 86; 100% vs. 96% vs. 97%). Conclusions: Our automated FP grading system combines high-level accuracy with cost- and time-effectiveness. Our algorithm may accelerate the grading process in FP patients and facilitate the FP surgeon's workflow. [ABSTRACT FROM AUTHOR]

We show that the differential equation for the three-loop equal-mass banana integral can be cast into an ε-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. The ε-factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter ε. The alphabet of the iterated integrals contains six letters. [ABSTRACT FROM AUTHOR]

We give a correspondence between automorphic pairs of distributions on R and Dirichlet series satisfying functional equations and some additional analytic conditions. Moreover, we show that the notion of automorphic pairs of distributions on R can be regarded as a generalization of automorphic distributions on smooth principal series representations of the universal covering group of SL(2,R). As an application, we prove Weil type converse theorems for automorphic distributions and Maass forms of real weight. [ABSTRACT FROM AUTHOR]

Let X be a complex smooth quasi-projective surface acted upon by a finite group G such that the quotient |$X/G$| has singularities only of ADE type. We obtain an explicit expression for the generating series of the Euler characteristics of the zero-dimensional components in the moduli space of zero-dimensional subschemes of X invariant under the action of G. We show that this generating series (up to a suitable rational power of the formal variable) is a holomorphic modular form. [ABSTRACT FROM AUTHOR]

For two varieties of dimension 5 constructed as double covers of P 5 branched along the union of 12 hyperplanes, we prove that the number of points over F p can be expressed in terms of Artin symbols and the pth Fourier coefficients of modular forms. Many analogous results are known in dimension ≤ 3 , but very few in higher dimension. In addition, we use an idea of Burek to construct quotients of our varieties for which the point counts mod p are expressible in terms of Artin symbols and the coefficients of a single modular form of weight 6. [ABSTRACT FROM AUTHOR]

This paper describes the use of impulse control of an acoustic field to create complex and precise particle patterns and then dynamically manipulate them. We first demonstrate that the motion of a particle in an acoustic field depends on the applied impulse and three distinct regimes can be identified. The high impulse regime is the well established mode where particles travel to the force minima of an applied continuous acoustic field. In contrast acoustic field switching in the low impulse regime results in a force field experienced by the particle equal to the time weighted average of the constituent force fields. We demonstrate via simulation and experiment that operating in the low impulse regime facilitates an intuitive and modular route to forming complex patterns of particles. The intermediate impulse regime is shown to enable more localised manipulation of particles. In addition to patterning, we demonstrate a set of impulse control tools to clear away undesired particles to further increase the contrast of the pattern against background. We combine these tools to create high contrast patterns as well as moving and re-configuring them. These techniques have applications in areas such as tissue engineering where they will enable complex, high fidelity cell patterns. [ABSTRACT FROM AUTHOR]

We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over quadratic progressions. Our reduction provides an analogue for the compact case of a criterion established by Luo–Sarnak for the case of the non-compact modular surface. The novelty is that known proofs of such criteria have depended crucially upon Fourier expansions, which are not available in the compact case. Unconditionally, we establish a twisted variant of the Holowinsky–Soundararajan theorem involving restrictions of normalized Hilbert modular forms arising via base change. [ABSTRACT FROM AUTHOR]

Given a congruence of Hecke eigenvalues between newforms f and g of odd, square free level, and weight 2 κ - 2 , with even κ ≥ 6 , we show that, under weak conditions, there is a congruence of Fourier coefficients between corresponding newforms of half-integral weight. [ABSTRACT FROM AUTHOR]

In this paper we generalize a well-known isomorphism between the space of cusp forms of weight k for a Fuchsian subgroup of the first kind Γ ⊂ SL 2 (R) and the space of certain Maaß forms of weight k for Γ to an isomorphism between the space of Siegel cusp forms of weight k for a subgroup Γ ⊂ Sp n (R) , which is commensurable with the Siegel modular group Sp n (Z) , and a suitable space of Siegel–Maaß forms of weight k for Γ . [ABSTRACT FROM AUTHOR]

Let $p_{\{3, 3\}}(n)$ denote the number of $3$ -regular partitions in three colours. Da Silva and Sellers ['Arithmetic properties of 3-regular partitions in three colours', Bull. Aust. Math. Soc.104(3) (2021), 415–423] conjectured four Ramanujan-like congruences modulo $5$ satisfied by $p_{\{3, 3\}}(n)$. We confirm these conjectural congruences using the theory of modular forms. [ABSTRACT FROM AUTHOR]

In this paper, we obtain two analogues of the Sturm bound for modular forms in the function field setting. In the case of mixed characteristic, we prove that any harmonic cochain is uniquely determined by an explicit finite number of its first Fourier coefficients where our bound is much smaller than the ones in the literature. A similar bound is derived for generators of the Hecke algebra on harmonic cochains. As an application, we present a computational criterion for checking whether two elliptic curves over the rational function field F q (θ) with same conductor are isogenous. In the case of equal characteristic, we also prove that any Drinfeld modular form is uniquely determined by an explicit finite number of its first coefficients in the t -expansion. [ABSTRACT FROM AUTHOR]

For fixed positive integers k and N, there are only finitely many holomorphic eta quotients of weight k for the congruence subgroup \(\Gamma_{0}(N)\). In this article, we obtain a similar finiteness result for holomorphic generalized eta quotients of weight k on \(\Gamma_1(p)\) where k is a positive integer and p is a prime number. We also obtain a criterion for two holomorphic generalised eta quotients which represent the same one. [ABSTRACT FROM AUTHOR]

This review mainly studies the development status, limitations, and future directions of modular microfluidic systems. Microfluidic technology is an important tool platform for scientific research and plays an important role in various fields. With the continuous development of microfluidic applications, conventional monolithic microfluidic chips show more and more limitations. A modular microfluidic system is a system composed of interconnected, independent modular microfluidic chips, which are easy to use, highly customizable, and on-site deployable. In this paper, the current forms of modular microfluidic systems are classified and studied. The popular fabrication techniques for modular blocks, the major application scenarios of modular microfluidics, and the limitations of modular techniques are also discussed. Lastly, this review provides prospects for the future direction of modular microfluidic technologies. [ABSTRACT FROM AUTHOR]

In this paper, using some results on the deletion correcting codes, we give an equivalent form of the Modular Subset-Sum Problem which is of significant importance in computer science and (quantum) cryptography. We also, using Ramanujan sums and their properties, give an explicit formula for the size of the Levenshtein code which has found many interesting applications, for examples, in studying DNA-based data storage and distributed message synchronization. [ABSTRACT FROM AUTHOR]

We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups. The tower discloses the role of codes in representation theory. [ABSTRACT FROM AUTHOR]

The goal of the present paper is to show that all the zeros of the Eisenstein series for Γ 0 ∗ (5) and Γ 0 ∗ (7) on the standard fundamental domain lie on the lower boundary arcs. These are improvements of the results in Shigezumi (Kyushu J Math 61:527–549, 2007). [ABSTRACT FROM AUTHOR]

In recent work, Miezaki introduced the notion of a sphericalT-design in R 2 , where T is a potentially infinite set. As an example, he offered the Z 2 -lattice points with fixed integer norm (a.k.a. shells). These shells are maximal spherical T-designs, where T = Z + \ 4 Z + . We generalize the notion of a spherical T-design to special ellipses, and extend Miezaki's work to the norm form shells for rings of integers of imaginary quadratic fields with class number 1. [ABSTRACT FROM AUTHOR]

Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application of the U-operator. The proofs of these theorems originally relied on the theory of harmonic Maass forms. Ahlgren and Samart obtained strengthened versions of these results using the theory of holomorphic modular forms. Here, we use such techniques to express all weight 2 CM newforms which are eta quotients as p-adic limits. In particular, we show that these forms are p-adic limits of the derivatives of the Weierstrass mock modular forms associated to their elliptic curves. [ABSTRACT FROM AUTHOR]

Although we can measure muscle activity and analyze their activation patterns, we understand little about how individual muscles affect the joint torque generated. It is known that they are controlled by circuits in the spinal cord, a system much less well-understood than the cortex. Knowing the contribution of the muscles toward a joint torque would improve our understanding of human limb control. We present a novel framework to examine the control of biomechanics using physics simulations informed by electromyography (EMG) data. These signals drive a virtual musculoskeletal model in the Neurorobotics Platform (NRP), which we then use to evaluate resulting joint torques. We use our framework to analyze raw EMG data collected during an isometric knee extension study to identify synergies that drive a musculoskeletal lower limb model. The resulting knee torques are used as a reference for genetic algorithms (GA) to generate new simulated activation patterns. On the platform the GA finds solutions that generate torques matching those observed. Possible solutions include synergies that are similar to those extracted from the human study. In addition, the GA finds activation patterns that are different from the biological ones while still producing the same knee torque. The NRP forms a highly modular integrated simulation platform allowing these in silico experiments. We argue that our framework allows for research of the neurobiomechanical control of muscles during tasks, which would otherwise not be possible. [ABSTRACT FROM AUTHOR]

The college English teaching model from the perspective of the Internet of Things is to introduce technology into the teaching process of college English. There are mainly students, teachers, and knowledge classrooms. The relationship between these roles in college English teaching is analyzed and researched. Then observing the wireless communication of the Internet of Things to manage the complex teaching management model in a hierarchical and modular form. A college English teaching model that is, constructs a student-centered, hierarchical classroom teaching model. Strengthen the cultivation of students' language application ability through the perception of English language and comprehensive language communication. And through the analysis of the understanding of the Internet of Things and the modules of college English teaching, the students, teachers, and knowledge in the classroom are organized in the classroom as a whole. The experimental results in this paper show that through the application of Internet of Things technology in college English teaching, students' English learning ability improves by 15–18%. [ABSTRACT FROM AUTHOR]

We show how our p-adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is the use of "moduli-friendly" Eisenstein series introduced by Makdisi, which allow us to evaluate modular forms at p-adic points of modular curves and dispenses us of the need for equations of modular curves and for q-expansion computations in the construction of models of modular Jacobians. The resulting algorithm compares very favourably to our complex-analytic method. [ABSTRACT FROM AUTHOR]

For each d ∈ N , we establish an infinite family of weight 1/2 quantum modular forms from the overpartition M d -rank generating function. Infinite quantum families from both the Dyson rank overpartition generating function and the overpartition M 2 -rank generating function appear as special cases of our work. As a corollary, we obtain explicit closed expressions which may be used to evaluate Eichler integrals of certain weight 3/2 theta functions. [ABSTRACT FROM AUTHOR]

In this study, the development of a multi-layer marking toolkit was investigated to improve construction quality and mitigate the problem of irregular designs in the layout-printing work performed at construction sites. The quality of conventional layout-printing work is dependent on the skill of the worker, and construction quality can suffer owing to inconsistencies in drawings resulting from human error. In this study, these problems were analyzed, and a construction-site-layout-marking toolkit apparatus and mechanical unit, with a structure that allowed for multi-layer installation for automated implementation at construction sites, were developed. The marking toolkit and mechanical unit with the multi-layer structure were developed in a modular form so that each module can operate independently. Furthermore, each module was developed in manual mode to improve the system by acquiring information on the movement of the marking toolkit and multi-layer structure. Additionally, data on the layout-printing method was developed by connecting the system via Ethernet and operating a wireless joystick. Finally, experiments were performed on a road surface covered with B4 paper and concrete panels to confirm the operational feasibility of the system, which was developed to operate manually. [ABSTRACT FROM AUTHOR]

We consider a natural basis for the space of weakly holomorphic modular forms for Γ0+(3). We prove that for some of the basis elements, if z0 in the fundamental domain for Γ0+(3) is one of zeroes of the elements, then either z0 is transcendental or is in .... [ABSTRACT FROM AUTHOR]

In 1981, Zagier conjectured that the Lambert series associated to the weight 12 cusp form Δ should have an asymptotic expansion in terms of the nontrivial zeros of the Riemann zeta function. This conjecture was proven by Hafner and Stopple. In 2017 and 2019, Chakraborty et al. established an asymptotic relation between Lambert series associated to any primitive cusp form (for full modular group, congruence subgroup and in Maass form case) and the nontrivial zeros of the Riemann zeta function. In this paper, we study Lambert series associated with primitive Hilbert modular form and establish similar kind of asymptotic expansion. [ABSTRACT FROM AUTHOR]

Let f ∈ k (S L 2 (ℤ)) be a normalized cuspidal Hecke eigenform. We give explicit formulas for weighted averages of the rightmost critical values of triple product L -functions L (s , f ⊗ g ⊗ h) , where g and h run over an orthogonal basis of k (S L 2 (ℤ)) consisting of normalized cuspidal Hecke eigenforms. Those explicit formulas provide us an arithmetic expression of the rightmost critical value of the individual triple product L -functions. [ABSTRACT FROM AUTHOR]

In this paper, we give an upper bound of the orders of Jacobi forms. For each fixed weight k , the growth rate of our upper bound divided by the index m as m goes to infinity is zero. Applying this result to Siegel paramodular forms, we know that the space of all formal series of Jacobi forms is finite dimensional. [ABSTRACT FROM AUTHOR]

We show that the results we had previously obtained on diagonals of 9- and 10-parameter families of rational functions in three variables x , y , and z , using creative telescoping, yielding modular forms expressed as pullbacked 2 F 1 hypergeometric functions, can be obtained much more efficiently by calculating the j -invariant of an elliptic curve canonically associated with the denominator of the rational functions. These results can be drastically generalized by changing the parameters into arbitrary rational functions of the product p = x y z . In other cases where creative telescoping yields pullbacked 2 F 1 hypergeometric functions, we extend this algebraic geometry approach to other families of rational functions in three or more variables. In particular, we generalize this approach to rational functions in more than three variables when the denominator can be associated to an algebraic variety corresponding to products of elliptic curves, or foliations in elliptic curves. We also extend this approach to rational functions in three variables when the denominator is associated with a genus-two curve such that its Jacobian is a split Jacobian, corresponding to the product of two elliptic curves. We sketch the situation where the denominator of the rational function is associated with algebraic varieties that are not of the general type, having an infinite set of birational automorphisms. We finally provide some examples of rational functions in more than three variables, where the telescopers have pullbacked 2 F 1 hypergeometric solutions, because the denominator corresponds to an algebraic variety that has a selected elliptic curve. [ABSTRACT FROM AUTHOR]

In this paper, we address the case of a particular class of function referred to as the rational equivariant functions. We investigate which elliptic zeta functions arising from integrals of power of ℘, where ℘ is the Weierstrass ℘-function attached to a rank two lattice of C , yield rational equivariant functions. Our concern in this survey is to provide certain examples of rational equivariant functions. In this sense, we establish a criterion in order to determine the rationality of equivariant functions derived from ratios of modular functions of low weight. Modular forms play an important role in number theory and many areas of mathematics and physics. [ABSTRACT FROM AUTHOR]

Let π$\pi$ be a cuspidal automorphic representation of GSp4(AQ)$\operatorname{GSp}_4(\mathbf {A}_\mathbf {Q})$, whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If π$\pi$ is not CAP or endoscopic, then we show that its associated ℓ$\ell$‐adic Galois representations are irreducible and crystalline for 100%$100\%$ of primes ℓ$\ell$. If, moreover, π$\pi$ is neither an automorphic induction nor a symmetric cube lift, then we show that, for 100%$100\%$ of primes ℓ$\ell$, the image of its mod ℓ$\ell$ Galois representation contains Sp4(Fℓ)$\operatorname{Sp}_4(\mathbf {F}_\ell)$. [ABSTRACT FROM AUTHOR]