The minimal generating set of the presentation ideal of Backelin semigroup ring

Let $K$ be a field, and let n1, ..., nr be positive integers. The Ideal of relations of the semigroup ring K[x1, ..., xr] generated by n1,..., nr is P(n1,..., nr) = {f(x1,...,xr): f(x1,...,xr) \in K[x1,...,xr], f(t^{n1}, ... ,t^{nr}) = 0} with t is transcendental over K. In 1970, Herzog showed that the least upper bound on the number of generators of $P(n1,..., nr) for r=3 is 3. In 1975, Bresinsky showed that the lowest upper bound on the number of generators of P(n1,..., nr)$, can be arbitrarily large if r \u3e=4. More recently, Herzog and Stamate provided a closed form for the number of generators for the semigroup ring in Bresinsky’s example, and showed that in this case, the number of generators for the semigroup ring is arbitrarily large but even. Progress have been made in finding a closed form for the number of generators of ideal of relations for various semigroup rings with four or more generators. All established work on this subject produced examples where this number is always an even number. However, in 2017, Stamate considered a semigroup suggested by Backelin, which has the following structure \u3c r(3n+2)+3, r(3n+2)+6, r(3n+2)+3n+4, r(3n+2)+3n+5 \u3e where n \u3e= 2 and r \u3e= 3n+2. Stamate reports that, computations using Singular and GAP (Groups, Algorithms, Programming - a System for Computational Discrete Algebra) indicate that the number of generators for this semigroup is 3n+4, which can be an odd number. In 2018 we showed that the conjecture holds for the special case where n=2. In this work, we prove that the result holds for any n

The generic crystallographic phase retrieval problem

In this paper we consider the problem of recovering a signal $x \in \mathbb{R}^N$ from its power spectrum assuming that the signal is sparse with respect to a generic basis for $\mathbb{R}^N$. Our main result is that if the sparsity level is at most $\sim\! N/2$ in this basis then the generic sparse vector is uniquely determined up to sign from its power spectrum. We also prove that if the sparsity level is $\sim\! N/4$ then every sparse vector is determined up to sign from its power spectrum. Analogous results are also obtained for the power spectrum of a vector in $\mathbb{C}^N$ which extend earlier results of Wang and Xu \cite{arXiv:1310.0873}.Comment: 20 page

Reduced-order Aeroelastic Model for Limit-cycle Oscillations in Vortex-dominated Unsteady Airfoil Flows

In previous research, Ramesh et al (JFM,2014) developed a low-order discrete vortex method for modeling unsteady airfoil flows with intermittent leading edge vortex (LEV) shedding using a leading edge suction parameter (LESP). LEV shedding is initiated using discrete vortices (DVs) whenever the Leading Edge Suction Parameter (LESP) exceeds a critical value. In subsequent research, the method was successfully employed by Ramesh et al (JFS, 2015) to predict aeroelastic limit-cycle oscillations in airfoil flows dominated by intermittent LEV shedding. When applied to flows that require large number of time steps, the computational cost increases due to the increasing vortex count. In this research, we apply an amalgamation strategy to actively control the DV count, and thereby reduce simulation time. A pair each of LEVs and TEVs are amalgamated at every time step. The ideal pairs for amalgamation are identified based on the requirement that the flowfield in the vicinity of the airfoil is least affected (Spalart, 1988). Instead of placing the amalgamated vortex at the centroid, we place it at an optimal location to ensure that the leading-edge suction and the airfoil bound circulation are conserved. Results of the initial study are promising

Modeling intermittent leading-edge vortex shedding in unsteady airfoil flows with reduced-count discrete vortices

A discrete-vortex method for unsteady airfoil flows with intermittent leading-edge vortex (LEV) shedding was proposed by Ramesh et al. (JFM, 2014). Two novelties were introduced: (i) LEV shedding is initiated using discrete vortices whenever the Leading Edge Suction Parameter (LESP), which is a measure of leading-edge suction, exceeds a critical value, and (ii) the strength of the discrete vortices is determined such that the LESP maintained at the critical value during the shedding process. Although results from this low-order method agree with CFD and experiments, the increasing vortex count with time increases the computational cost. The large number of shed vortices from the TE can be reduced through traditional techniques such as amalgamation and deletion, as they typically convect away from the airfoil and interact only weakly with the airfoil vorticity. The LEV, on the other hand, interacts strongly with the airfoil, and has a large influence on the forces. An approach to reduce the vortex count is desired. Inspired by Wang and Eldredge (TCFD, 2013), we propose a model that has just a single vortex to model an active LEV. The varying strength of this free vortex is determined using our LESP criterion. Results from the method for unsteady airfoil motions are promising

Phase retrieval with semi-algebraic and ReLU neural network priors

The key ingredient to retrieving a signal from its Fourier magnitudes, namely, to solve the phase retrieval problem, is an effective prior on the sought signal. In this paper, we study the phase retrieval problem under the prior that the signal lies in a semi-algebraic set. This is a very general prior as semi-algebraic sets include linear models, sparse models, and ReLU neural network generative models. The latter is the main motivation of this paper, due to the remarkable success of deep generative models in a variety of imaging tasks, including phase retrieval. We prove that almost all signals in R^N can be determined from their Fourier magnitudes, up to a sign, if they lie in a (generic) semi-algebraic set of dimension N/2. The same is true for all signals if the semi-algebraic set is of dimension N/4. We also generalize these results to the problem of signal recovery from the second moment in multi-reference alignment models with multiplicity free representations of compact groups. This general result is then used to derive improved sample complexity bounds for recovering band-limited functions on the sphere from their noisy copies, each acted upon by a random element of SO(3)

R20. Development of sustained release gastroretentive floating tablets using HME coupled 3D printing: A QbD approach

Corresponding author (Pharmaceutics and Drug delivery): Nagireddy Dumpa, [email protected]://egrove.olemiss.edu/pharm_annual_posters/1019/thumbnail.jp

An Effective Deep Learning Based Multi-Class Classification of DoS and DDoS Attack Detection

In the past few years, cybersecurity is becoming very important due to the rise in internet users. The internet attacks such as Denial of service (DoS) and Distributed Denial of Service (DDoS) attacks severely harm a website or server and make them unavailable to other users. Network Monitoring and control systems have found it challenging to identify the many classes of DoS and DDoS attacks since each operates uniquely. Hence a powerful technique is required for attack detection. Traditional machine learning techniques are inefficient in handling extensive network data and cannot extract high-level features for attack detection. Therefore, an effective deep learning-based intrusion detection system is developed in this paper for DoS and DDoS attack classification. This model includes various phases and starts with the Deep Convolutional Generative Adversarial Networks (DCGAN) based technique to address the class imbalance issue in the dataset. Then a deep learning algorithm based on ResNet-50 extracts the critical features for each class in the dataset. After that, an optimized AlexNet-based classifier is implemented for detecting the attacks separately, and the essential parameters of the classifier are optimized using the Atom search optimization algorithm. The proposed approach was evaluated on benchmark datasets, CCIDS2019 and UNSW-NB15, using key classification metrics and achieved 99.37% accuracy for the UNSW-NB15 dataset and 99.33% for the CICIDS2019 dataset. The investigational results demonstrate that the suggested approach performs superior to other competitive techniques in identifying DoS and DDoS attacks

Dental professionals’ knowledge and behavior towards utilization of gloves: a cross-sectional survey

Introduction: The purpose of this study was to assess the perception and beliefs of dental healthcare providers towards usage of different type of gloves.Methods: A self-administered questionnaire was distributed among a total of 241 participants out of which 198 participants (77 interns, 58 dental post-graduate students (PG) and 63 dental faculty members) returned completed questionnaire (response rate of 82.15%). The questionnaire comprised of questions on dental professionals’ preferences for certain types of gloves and the reasons for these preferences, as well as determining their knowledge, beliefs and behavior concerning the use of dental gloves as a means of barrier protection.Results: Dental faculty members had a better knowledge regarding use of gloves as compared to dental PG students and interns. Most of the study participants preferred certain types of gloves for the purpose of better protection followed by comfort. Most of the participants believed that gloves provide full protection as long as there is no visible tear (interns 70.1%; PG students 50%; faculty members 60.3%). Most of the interns (42.9%) and PG students (41.4%) did not know about the fact that petroleum based products affect the integrity of the gloves. 2.6% interns, 29.3% PG students and 20.6% faculty members reported that they would not change gloves during an uninterrupted three-hour long procedure.Conclusion: Most of the interns and PG students had poor knowledge regarding usage of gloves which calls for an action on the part of educators to educate and train dental professionals regarding proper infection control practices