Restriction Operators Research Articles

RESTRICTED AND EXTENDED THETA OPERATIONS OF SOFT SETS: NEW RESTRICTED AND EXTENDED SOFT SET OPERATIONS

Since its introduction by Molodtsov in 1999, soft set theory has gained widespread recognition as a method for addressing uncertainty-related issues and modeling uncertainty. It has been used to solve several theoretical and practical issues. Since its introduction, the central idea of the theory-soft set operations-has captured the attention of scholars. Numerous limited and expanded businesses have been identified, and their attributes have been scrutinized thus far. We present a detailed analysis of the fundamental algebraic properties of our proposed restricted theta and extended theta operations, which are unique restricted and extended soft set operations. We also investigate these operations’ distributions over various kinds of soft set operations. We demonstrate that, when coupled with other types of soft set operations, the extended theta operation forms numerous significant algebraic structures, such as semirings in the collection of soft sets over the universe, by taking into account the algebraic properties of the extended theta operation and its distribution rules. This theoretical subject is very important from both a theoretical and practical perspective since soft sets' operations form the foundation for numerous applications, including cryptology and decision-making procedures.

Rates and Risk Factors for 30-Day Morbidity After One-Stage Vertical Banded Gastroplasty Conversions: A Retrospective Analysis.

Background: The vertical banded gastroplasty (VBG) is a historic restrictive bariatric operation often requiring further surgery. In this investigation utilizing the 2021 Metabolic and Bariatric Surgery Accreditation and Quality Improvement Program (MBSAQIP) national dataset, we aim to better define the outcomes of VBG conversions.Methods: We queried the 2021 MBSAQIP dataset for patients who underwent a conversion from a VBG to Roux-en-Y gastric bypass (RYGB) or sleeve gastrectomy (SG). Demographics, comorbidities, laboratory values, and additional patient factors were examined. Rates of key consequential outcome measures 30-day readmission, reoperation, reintervention, mortality, and a composite endpoint (at least 1 of the 4) were further calculated.Results: We identified 231 patients who underwent conversion from VBG to SG (n = 23), RYGB (n = 208), or other anatomy (n = 6), of which 93% of patients were female, and 22% of non-white race. The median age was 56years and body-mass index (BMI) was 43kg/m2. The most common surgical indications included weight considerations (48%), reflux (25%), anatomic causes (eg, stricture, fistula, and ulcer; 10%), and dysphagia (6.5%). Thirty-day morbidity rates included reoperation (7.8%), readmission (9.1%), reintervention (4.3%), mortality (.4%), and the composite endpoint (15%). Upon bivariate analysis, we did not identify any specific risk factor for the 30-day composite endpoint.Discussion: One-stage VBG conversions to traditional bariatric anatomy are beset with higher 30-day morbidity relative to primary procedures. Additional MBSAQIP data will be required for aggregation, to better characterize the risk factors inherent in these operations.

On Numerical Radius Inequalities for Hilbert Space Operators

This paper aims to find special cases of some inequalities for numerical radii and spectral radii of a bounded linear operator on a Hil-bert space, we focus on numerical radii inequalities for restricted linear operators on complex Hil-bert spaces for the case of one and two operators, and study the numerical range of an operator K on a complex Hil-bert space H, after that we present some inequalities for numerical radii and spectral radii and studied it to find new results. At the end of this paper we find several inequalities for numerical radii by using the spectral norm, this study is necessary to find other bound for zeros of polynomials and this study is necessary to find new bounds for the zeros of polynomials by a playing the new results to the companion matrix.

Fast algebraic multigrid for block-structured dense systems arising from nonlocal diffusion problems

Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large structured systems of equations. However, how to build/check restriction and prolongation operators in practical AMG methods for nonsymmetric structured systems is still an interesting open question in its full generality. The present paper deals with the block-structured dense and Toeplitz-like-plus-cross systems, including nonsymmetric indefinite and symmetric positive definite (SPD) ones, arising from nonlocal diffusion problems. The simple (traditional) restriction operator and prolongation operator are employed in order to handle such block-structured dense and Toeplitz-like-plus-cross systems, which are convenient and efficient when employing a fast AMG. We provide a detailed proof of the two-grid convergence of the method for the considered SPD structures. The numerical experiments are performed in order to verify the convergence with a computational cost of only O(NlogN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(N \ ext{ log } N)$$\\end{document} arithmetic operations, by exploiting the fast Fourier transform, where N is the number of the grid points. To the best of our knowledge, this is the first contribution regarding Toeplitz-like-plus-cross linear systems solved by means of a fast AMG.

Hepatic artery restriction operation combined with ALPPS (HARO-ALPPS), a novel ALPPS procedure for the treatment of hepatocellular carcinoma with severe fibrosis: retrospective clinical cohort study.

Associating liver partition with portal vein ligation for staged liver resection (ALPPS) has been used in the treatment of patients with advanced or massive liver cancer without sufficient future liver remnant, but concerns remain regarding tumor outcomes and surgical safety. This study aims to evaluate the efficacy and safety of a new procedure, hepatic artery restriction operation combined with ALPPS (HARO-ALPPS), in the treatment of hepatocellular carcinoma (HCC) patients especially with severe fibrosis. This retrospective study analyzed 8 patients who underwent HARO-ALPPS for HCC and compared their outcomes with 64 patients who underwent conventional ALPPS. The primary outcomes assessed were liver regeneration ability (measured by relative and absolute kinetic growth rates), postoperative complications, and mortality. The secondary outcomes included overall survival and disease-free survival. HARO-ALPPS significantly restricted the blood supply of the hepatic artery. One week after surgery, the blood flow of the right hepatic artery dropped to 62.1%. At the same time, HARO-ALPPS shows superior liver regeneration ability, which is particularly prominent in the background of liver fibrosis. No serious complications occurred after HARO-ALPPS. The overall survival rate of HARO-ALPPS was 75%, which was higher than that of ALPPS (64%, P =0.816). Compared to conventional ALPPS, HARO-ALPPS exhibits a better liver regeneration ability, and favorable long-term outcomes. Further prospective studies are needed to validate these findings and evaluate the long-term oncologic outcomes of this novel procedure.

3D printing hybrid-fiber reinforced engineered cementitious composites (3DP-HECC): Feasibility in long-open-time applications

Hybridization of multi-scale and multi-functional fibers to generate Hybrid-fiber Engineered Cementitious Composites (HECC) offers a promising approach for enhancing ECC in 3D printing (3DP), addressing limitations such as restricted build-up height and operation time. This study strategically combined polyethylene (PE) fiber (1.0 %), steel fiber (0.5 %) and cellulose filaments (CF) at various dosages (0–0.25 %) to investigate the evolution of rheological behavior over different time intervals (0–60 min with 15 min intervals) and optimize the printability of 3DP-HECC with long-open-time. Incorporating of CF or steel fiber enhanced static yield stress, dynamic yield stress and plastic viscosity, particularly benefiting buildability with steel fiber inclusion. Moreover, CF integration effectively moderated the growth rates of static yield stress and dynamic yield stress while maintaining thixotropic index, mitigating extrusion defects and extending operation time to 60 min for structure-level printing. Conversely, steel fiber exhibited contrasting behavior. By integrating the evolution of time-dependent rheological parameters and practical printing observations, an optimum CF dosage of 0.20 % was identified for high-quality 3DP with superior build-up layers. Finally, a fiber hybridization strategy was suggested to optimize the printability of 3DP-HECC, providing theoretical guidance for implementing high-quality applications with extended operation time.

Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems. We show that the associated regularized linear sampling indicator converges to the average of the unknown in a small neighborhood as the regularization parameter approaches to zero. We develop both a shape identification theory and a parameter identification theory which are stimulated, analyzed, and implemented with the help of the prolate spheroidal wave functions and their generalizations. We further propose a prolate-based implementation of the linear sampling method and provide numerical experiments to demonstrate how this linear sampling method is capable of reconstructing both the shape and the parameter.

Lossless Phase‐Change Material Enabled Wideband High‐Efficiency Spatial Light Phase Modulation at Near‐Infrared

AbstractHigh‐efficiency spatial light phase modulation with wide operating bandwidth is highly significant yet challenging. Dynamic metasurfaces leveraging active materials with tunable optical response provide a promising solution. Current work is generally confronted with restricted operation bandwidth and diminished modulation efficiency, constrained by the limited tunable range and inherent absorption of active materials particular at optical frequency. Recently, the emergence of lossless phase‐change material Sb2Se3 has garnered widespread attention. Its unique characteristics, including near‐zero absorption at near‐infrared and a substantial refractive index contrast ≈0.93 during phase transition, enable the possibility of high‐performance spatial light modulation. Pioneering studies have validated the capability of lossless phase‐change metasurfaces for wavefront control, but are typically restricted to limited efficiency. Here, a hybrid phase‐change metasurface utilizing over‐coupled resonances supported by Sb2Se3 nanoholes is proposed. For the first time in optical frequency, high‐efficiency 4‐level phase modulation covering over π range is experimentally demonstrated with a sizable operating bandwidth of 42 nm and a minimum reflectance of exceeding 0.5. Leveraging optically driven localized phase‐transition technique, dynamic beam deflection is further demonstrated. The work validates the tremendous potential of phase‐change metasurfaces in achieving advanced spatial light control, signifying significant progress for the development and application of phase‐change photonic devices.

Non-numerical weakly relational domains

The weakly relational domain of Octagons offers a decent compromise between precision and efficiency for numerical properties. Here, we are concerned with the construction of non-numerical relational domains. We provide a general construction of weakly relational domains, which we exemplify with an extension of constant propagation by disjunctions. Since for the resulting domain of 2-disjunctive formulas satisfiability is NP-complete, we provide a general construction for a further, more abstract, weakly relational domain where the abstract operations of restriction and least upper bound can be efficiently implemented. In the second step, we consider a relational domain that tracks conjunctions of inequalities between variables, and between variables and constants for arbitrary partial orders of values. Examples are sub(multi)sets, as well as prefix, substring or scattered substring orderings on strings. When the partial order is a lattice, we provide precise polynomial algorithms for satisfiability, restriction, and the best abstraction of disjunction. Complementary to the constructions for lattices, we find that, in general, satisfiability of conjunctions is NP-complete. We therefore again provide polynomial abstract versions of restriction, conjunction, and join. By using our generic constructions, these domains are extended to weakly relational domains that additionally track disjunctions. For all our domains, we indicate how abstract transformers for assignments and guards can be constructed.

Role of buttering layer composition on microstructural heterogeneity and mechanical properties of Alloy 617 and P92 steel dissimilar welded joints for future Indian AUSC program

Restrictive operating conditions (even exceeding 700 °C) of materials in advanced ultra super critical (AUSC) power plants and the need to minimize manufacturing and maintenance costs require the production of dissimilar metal welded joints (DMW). Significant differences in the physical and chemical properties of welded materials lead to phenomena that reduce the weldability of the metals used and force the search for solutions that limit unfavorable phenomena, e.g., the use of buttering layers. The study presents a comparison of two types of joints with Alloy 617 (UNS N06617) and ferritic P92 (UNS K92460) steel made using Inconel 82 (ENiCrFe-3) and Inconel 617 (ERNiCrCoMo-1) alloys buttering layer and the corresponding chemical composition of filler metals. All areas of the joints made with the gas tungsten arc welding process were subjected to structural investigations (optical microscopy, scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS) and mechanical tests (microhardness, room and high temperature tensile, and toughness testing). Despite the more complicated welding procedure, sound welded joints were obtained with favorable properties resulting, inter alia, from the reduced thickness of the martensite layer in HAZ of P92 steel and the limited diffusion of alloy components compared to welded joints without the buttering layer. This also resulted in a reduction of the maximum hardness (especially in the case of Inconel 82 buttering—by 15–30 HV0.5 in comparison with Inconel 617 buttering) and an increase in strength while limiting the decrease in plasticity (even 663 MPa tensile strength and 21% of elongation for Inconel 617 buttered joint). Moreover, improved high-temperature performance (approximately 70–100 MPa) of the welded joint following the application of the buttering layer was confirmed. The presented results allow for drawing general conclusions that both proposed welding procedures can be recommended for use in the working conditions occurring at AUSC.

Preparing Future Military Medical Officers to Conduct Emergency Fresh Whole Blood Transfusions in Austere Environments: A Novel Training Curriculum.

Providing resilient Damage Control Resuscitation capabilities as close to the point of injury as possible is paramount to reducing mortality and improving patient outcomes for our nation's warfighters. Emergency Fresh Whole Blood Transfusions (EFWBT) play a critical role in supporting this capability, especially in future large-scale combat operations against peer adversaries with expected large patient volumes, restrictive operating environments, and unreliable logistical supply lines. Although there are service-specific training programs for whole blood transfusion, there is currently no dedicated EFWBT training for future military medical officers. To address this gap, we developed, implemented, and evaluated a training program to enhance EFWBT proficiency in third-year military medical students at the F. Edward Hebert School of Medicine at the USU. After reviewing both the 75th Ranger Regiment Ranger O-Low Titer program and the Marine Corps' Valkyrie program, along with the relevant Joint Trauma System Clinical Practice Guidelines, we created a streamlined and abbreviated training curriculum. The training consisted of both online preparatory materials as well as a 2-hour in-person training that included didactic and experiential learning components. Participants were 165 active duty third-year medical students at USU. Participants were assessed using a pre- and post-assessment self-reported questionnaire on their confidence in the practical application and administrative oversight requirements of an EFWBT program. Participants' performance was also assessed using a pre/post knowledge assessment consisting of 10 multiple choice questions identified as critical to understanding of the academic principles of EFWBT along with the baseline questionnaire. Differences in the mean scores of the pre- and post-assessment self-reported questionnaire (increased from 2.32 to 3.95) were statistically significant (P < .001). Similarly, there was a statistically significant improvement in student test scores, with the mean score increasing by approximately 3 points or 30%. There was no significant difference in student confidence assessment or test scores based on branch of service. Students who had previously deployed did not show a statistically significant difference in scores compared to students who had not previously deployed. Our results suggest that the implementation of streamlined EFWBT training into the undergraduate medical education of future military medical officers offers an efficient way to improve their baseline proficiency in EFWBTs. Future research is needed to assess the impact of this training on real-world applications in forward-deployed environments.

Multi-matrix correlators and localization

We study generating functions of 14\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{4} $$\\end{document}-BPS states in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super Yang-Mills at finite N by attempting to generalize the Harish-Chandra-Itzykson-Zuber integral to multiple commuting matrices. This allows us to compute the overlaps of two or more generating functions; such calculations arise in the computation of two-point correlators in the free-field limit. We discuss the four-matrix HCIZ integral in the U(2) context and lay out a prescription for finding a more general formula for N > 2. We then discuss its connections with the restricted Schur polynomial operator basis. Our results generalize readily to arbitrary numbers of matrices, opening up the opportunity to study more generic BPS operators.

Circulating power flow restricted operation of the isolated bi-directional dual-active bridge DC-DC converter for battery charging applications

This paper presents the Non-Circulating Power Flow (NCPF) enabled Dual Active Bridge (DAB) converter controller strategy. The proposed DAB controller eliminates the non-circulating power flow for all the four conventional modulation algorithms, i.e., Single Phase Shift (SPS), Extended Phase Shift (EPS), Dual Phase Shift (DPS) and Triple Phase Shift (TPS) modulation schemes. This leads to lesser current stress and power loss across the DAB converter switches due to reduced peak inverse current. The proposed controller strategy finds various applications, such as in a Solid-State Transformer (SST) enabled microgrid, or for Electric Vehicle (EV) Energy Storage Unit (ESU: battery, supercapacitor) integrations, etc. The proposed NCPF operation reduces battery (and supercapacitor) current stress by upto 71.8 %, and improves operative environment, thus fostering its health and lifecycle. In NCPF mode, if the rating of installed switches (current and voltage ratings) remains unchanged, its power transfer capability is marginally reduced by mere 10.0 %. In addition to this, the operating range (i.e., controlling range of phase shift (Φ) and modulation index (m)) remains unaffected. This paper summarizes the DAB NCPF operation in restricted power flow mode as a function of Φ and m through 3-D and 4-D graphs. Finally, working of NCPF DAB is tested via both simulation and hardware platforms. Comparative results are shown for conventional and proposed modulation schemes on hardware platform, to showcase the elimination of circulating current in both forward and reverse DAB operating modes. It is inferred that proposed controller is worthy of real-world implementations.

Fredholm Index of 3-Tuple of Restriction Operators and the Pair of Fringe Operators for Submodules in $$H^2({\mathbb {D}}^3)$$

Fredholm Index of 3-Tuple of Restriction Operators and the Pair of Fringe Operators for Submodules in $$H^2({\mathbb {D}}^3)$$

Single anastomosis sleeve ileal bypass a single anastomosis sleeve jejunal bypass in the surgical treatment of severe obesity.

Bariatric surgery has been proven to be an effective method in the treatement of morbid obesity. The ideal bariatric procedure should be effective, easy to perform and safe. Sleeve gastrectomy and RYGB currently represent the most frequently used bariatric/metabolic procedures. However, they have a certain percentage of complications and post-operative morbidity and also they fail in some patients. These facts lead to the development of new surgical procedures, which also include single anastomosis sleeve ileal bypass (SASI) and single anastomosis sleeve jejunal bypass (SASJ). These procedures combines the advantages of restrictive and malabsorptive operations at the same time reducing the risk of nutrient deficiencies by maintaining passage through all the alimentary tract. The results so far are encouraging, further research and especially longer-term results are necessary.

A New Soft Set Operation: Complementary Soft Binary Piecewise Lamda (λ) Operation

In 1999, Molodtsov introduced Soft Set Theory as a mathematical tool to deal with uncertainty. It has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations have been defined and used in various types. In this paper, we define a new kind of soft set operation called, “complementary soft binary piecewise lambda operation” and we handle its basic algebraic properties. Also, it is intended to contribute to the literature of soft set by gaining the relationships between this new soft set operation and some other types of soft set operations via examining the distribution of complementary soft binary piecewise lambda operation over extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations in order to inspire to obtain the algebaric structures of soft sets and some new decision making methods.

Algorithmic monotone multiscale finite volume methods for porous media flow

Multiscale finite volume methods are known to produce reduced systems with multipoint stencils which, in turn, could give non-monotone and out-of-bound solutions. We propose a novel solution to the monotonicity issue of multiscale methods. The proposed algorithmic monotone (AM- MsFV/MsRSB) framework is based on an algebraic modification to the original MsFV/MsRSB coarse-scale stencil. The AM-MsFV/MsRSB guarantees monotonic and within bound solutions without compromising accuracy for various coarsening ratios; hence, it effectively addresses the challenge of multiscale methods' sensitivity to coarse grid partitioning choices. Moreover, by preserving the near null space of the original operator, the AM-MsRSB showed promising performance when integrated in iterative formulations using both the control volume and the Galerkin-type restriction operators. We also propose a new approach to enhance the performance of MsRSB for MPFA discretized systems, particularly targeting the construction of the prolongation operator. Results show the potential of our approach in terms of accuracy of the computed basis functions and the overall convergence behavior of the multiscale solver while ensuring a monotone solution at all times.

A New Soft Set Operation: Complementary Soft Binary Piecewise Star (*) Operation

Soft set theory, introduced by Molodtsov, is as an important mathematical tool to deal with uncertainty and it has been conveyed to many fields both as theoretical and application aspect. Since its inception, different kinds of soft set operations are defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise star operation and we investigate its basic algebraic properties. Moreover, it is aimed to contribute to the soft set literature by obtaining the relationships between this new soft set operation and some other types of soft set operations by examing the distribution of complementary soft binary piecewise star operation over extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations

A parallel geometric multigrid method for adaptive topology optimization

This work presents an efficient parallel geometric multigrid (GMG) implementation for preconditioning Krylov subspace methods solving differential equations using non-conforming meshes for discretization. The approach does not constrain such meshes to the typical multiscale grids used by Cartesian hierarchical grid methods, such as octree-based approaches. It calculates the restriction and interpolation operators for grid transferring between the non-conforming hierarchical meshes of the cycle scheme. Using non-Cartesian grids in topology optimization, we reduce the mesh size discretizing only the design domain and keeping the geometry of boundaries in the final design. We validate the GMG method operating on non-conforming meshes using an adaptive density-based topology optimization method, which coarsens the finite elements dynamically following a weak material estimation criterion. The GMG method requires the generation of the hierarchical non-conforming meshes dynamically from the one used by the adaptive topology optimization to analyze to the one coarsening all the mesh elements until the coarsest level of the mesh hierarchy. We evaluate the performance of the adaptive topology optimization using the GMG preconditioner operating on non-conforming meshes using topology optimization on a fine-conforming mesh as the reference. We also test the strong and weak scaling of the parallel GMG preconditioner with two three-dimensional topology optimization problems using adaptivity, showing the computational advantages of the proposed method.

Homogenization of the unsteady compressible Navier-Stokes equations for adiabatic exponent γ > 3

We consider the unsteady compressible Navier-Stokes equations in a perforated three-dimensional domain, and show that the limit system for the diameter of the holes going to zero is the same as in the perforated domain provided the perforations are small enough. The novelty of this result is the lower adiabatic exponent γ>3 instead of the known value γ>6. The proof is based on the use of two different restriction operators leading to two different types of pressure estimates. We also discuss the extension of this result for the unsteady Navier-Stokes-Fourier system as well as the optimality of the known results in arbitrary space dimension for both steady and unsteady problems.