On the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B)

In this paper, we prove that the Ramanujan-Nagell type Diophantine equation (Dx^2+k^n=B) has at most three nonnegative integer solutions ((x, n)) for (k) a prime and (B, D) positive integers

On two Diophantine equations of Ramanujan-Nagell type

In this paper, we prove two conjectures of Ulas ([21]) on two Diophantine equations of Ramanujan-Nagell type. In fact, we show that the following equations x2+(2m+1+1)2n=24(m+1)+23(m+1)+22m+2m+1+1, x2+(22m+6-1)2n/3 = (49 · 42m+5-11· 4m+3+1)/9 have exactly four solutions

Study on Multi-step Forming Paths for Double Curved Parts of 1561 Aluminium Alloy

Recently, corrosion-resistant 1561 aluminium alloy has been widely applied to the production of curved parts. However, the sheets of this material will generate a high amount of springback during multi-point forming, which means that a large amount of springback compensation is required. In this paper, four multi-step forming paths are designed to study the effect of forming paths on the multi-point forming results of double curved parts for 1561 aluminium alloy. Numerical simulation of the multi-step forming of curved sheets is carried out by ABAQUS finite element simulation software. The simulation results indicate that the 1561 aluminium alloy double curved parts produce poor situations such as wrinkling and low forming accuracy in single-step forming, while the accuracy improves significantly and the forming quality increases after four-step forming. Therefore, a four-step forming path was adopted for stamping tests on double curved parts. The results of the accuracy inspection of the formed parts by Gom-inspect demonstrate that the quality of the curved parts can be effectively improved by four-step forming, which has a certain significance in guiding the forming preparation of parts for engineering applications

Quantitative evaluation of gut microbiota composition in pancreatic cancer: a pooled study

Background: Prior research has demonstrated a positive association between the composition of gut microbiota and the incidence of pancreatic cancer. Nevertheless, a thorough quantitative and systematic evaluation of the distinct properties of gut microbiota in individuals diagnosed with pancreatic cancer has yet to be conducted. The objective of this study is to examine alterations in the diversity of intestinal microbiota in individuals diagnosed with pancreatic cancer. Methods: Search for relevant literature published before July 2023 in 4 databases: PubMed, Embase, Web of Science, and Cochrane Library, without any language restrictions. Results: A total of 12 studies were included, including 535 patients with pancreatic cancer and 677 healthy controls. Analysis was conducted on 6 phyla, 16 genera, and 6 species. The study found significant and distinctive changes in the α-diversity of gut microbiota, as well as in the relative abundance of multiple gut bacterial groups at the phylum, genus, and species levels in pancreatic cancer patients. Conclusion: Overall, there are certain characteristic changes in the gut microbiota of pancreatic cancer patients. However, further research is warranted to elucidate the specific mechanism of action and the potential for treatment

Regional variation in NAFLD prevalence and risk factors among people living with HIV in Europe: a meta-analysis

Background and Aim: Europe faces an elevated risk of nonalcoholic fatty liver disease (NAFLD) among people living with HIV (PLWH), contributing to the region’s highest global burden of NAFLD. However, the prevalence of NAFLD across various European countries and regions remains unclear. This study aims to investigate the prevalence and risk factors associated with NAFLD among PLWH across European countries. Methods: A systematic search was conducted across four databases: PubMed, Embase, Web of Science, and Cochrane Library. Data on the prevalence of NAFLD, nonalcoholic steatohepatitis (NASH), and fibrosis, as well as the associated risk factors, were collected among PLWH in Europe. Results: Thirty-six studies from 13 European nations were included. The prevalence of NAFLD, NASH, and fibrosis were 42% (95%CI 37–48), 35% (95%CI 21–50) and 13% (95%CI 10–15), respectively. Male gender, BMI, waist circumference, Diabetes, hypertension, metabolic syndrome, dyslipidemia, triglycerides, HDL, LDL, ALT, AST, and years on antiretroviral therapy (ART) were found to be risk factors for NAFLD. High BMI and triglycerides were associated with NASH. Patients with high BMI and triglycerides are at increased risk of significant liver fibrosis. Conclusion: The high prevalence of NAFLD, NASH, and fibrosis among PLWH in Europe highlights the need for early screening, intervention, and increased research focus on adolescents living with HIV. Furthermore, the significant variations observed between countries and regions underscore the influence of related risk factors

Characterization and identification of the integrin family in silkworm, Bombyx mori

YesAs an important economic insect, Bombyx mori is also a useful model organism for lepidopteran insect. Integrins are evolutionarily conserved fromsponges to humans, and play vital roles inmany physiological and pathological processes. To explore their diverse functions of integrins in insect, eleven integrins including sixα and five β subunitswere cloned and characterized fromsilkworm. Our results showed that integrins fromsilkwormown more family members compared to other invertebrates. Among those α subunits, integrins α1, α2, and the other four subunits belong to PS1, PS2, and PS3 groups, respectively. The β subunits mainly gather in the insect βν group except the β1 subunit which belongs to the insect β group. Expression profiles demonstrated that the integrins exhibited distinct patterns, but were mainly expressed in hemocytes. α1 and β2 subunits are the predominant ones either in the embryogenesis or larva stages. Interestingly, integrins were significantly up-regulated after stimulated by 20-hydroxyecdysone (20-E) in vivo. These results indicate that integrins performdiverse functions in hemocytes of silkworm. Overall, our results provide a newinsight into the functional and evolutionary features of integrins.National Basic Research Programof China (No. 2012cb114603), the Research Fund for the Doctoral Program of Higher Education of China (20130182110003), the Natural Science Foundation of Chongqing (cstc2013jcyjys0007), and the Fundamental Research Funds for the Central Universities (SWU111014)

Signature of the coexistence of ferromagnetism and superconductivity at KTaO3_3 heterointerfaces

The coexistence of superconductivity and ferromagnetism is a long-standing issue in the realm of unconventional superconductivity due to the antagonistic nature of these two ordered states. Experimentally identifying and characterizing novel heterointerface superconductors that coexist with magnetism is challenging. Here, we report the experimental observation of long-range ferromagnetic order at the verge of two-dimensional superconductivity at KTaO$_3$ heterointerfaces. Remarkably, we observe in-plane magnetization hysteresis loop persisting up to room temperature with direct current superconducting quantum interference device measurements. Furthermore, first-principles calculations suggest that the observed robust ferromagnetism is attributed to the presence of oxygen vacancies that localize electrons in nearby Ta 5$d$ states. Our findings not only indicate KTaO$_3$ heterointerfaces as unconventional superconductors with time-reversal symmetry breaking, but also inject a new momentum to the study of the delicate interplay between superconductivity and magnetism boosted by strong spin-orbit coupling inherent to the heavy Ta in 5$d$ orbitals of KTaO$_3$ heterointerfaces.Comment: 7 pages, 3 figure

Low-Latency Design and Implementation of the Squaring in Class Groups for Verifiable Delay Function Using Redundant Representation

A verifiable delay function (VDF) is a function whose evaluation requires running a prescribed number of sequential steps over a group while the result can be efficiently verified. As a kind of cryptographic primitives, VDFs have been adopted in rapidly growing applications for decentralized systems. For the security of VDFs in practical applications, it is widely agreed that the fastest implementation for the VDF evaluation, sequential squarings in a group of unknown order, should be publicly provided. To this end, we propose a possible minimum latency hardware implementation for the squaring in class groups by algorithmic and architectural level co-optimization. Firstly, low-latency architectures for large-number division, multiplication, and addition are devised using redundant representation, respectively. Secondly, we present two hardware-friendly algorithms which avoid time-consuming divisions involved in calculations related to the extended greatest common divisor (XGCD) and design the corresponding low-latency architectures. Besides, we schedule and reuse these computation modules to achieve good resource utilization by using compact instruction control. Finally, we code and synthesize the proposed design under the TSMC 28nm CMOS technology. The experimental results show that our design can achieve a speedup of 3.6x compared to the state-of-the-art implementation of the squaring in the class group. Moreover, compared to the optimal C++ implementation over an advanced CPU, our implementation is 9.1x faster

Quantum metallic state in the titanium sesquioxide heterointerface superconductor

The emergence of the quantum metallic state marked by a saturating finite electrical resistance in the zero-temperature limit in a variety of two-dimensional superconductors injects a new momentum to the realm of unconventional superconductivity. Despite much research efforts over last few decades, there is not yet a general consensus on the nature of this unexpected quantum metal. Here, we report the unique quantum metallic state within the hallmark of Bose-metal characterized by the saturated resistance and simultaneously vanished Hall resistance in the titanium sesquioxide heterointerface superconductor Ti$_2$O$_3$/GaN. Strikingly, the quantum bosonic metallic state proximate to the two-dimensional superconductivity-metal transition tuned by magnetic fields persists in the normal phase, suggesting that the existence of composite bosons formed by electron Cooper pairs survives even in the normal phase. Our work marks the observation of the preformed electron Cooper pairs in heterointerface superconductor and sheds new light on understanding the underlying pairing mechanism of unconventional superconductivity.Comment: 6 pages, 4 figure

High-Speed Low-Power Viterbi Decoder Design for TCM Decoders

High-speed, low-power design of Viterbi decoders for trellis coded modulation (TCM) systems is presented in this paper. It is well known that the Viterbi decoder (VD) is the dominant module determining the overall power consumption of TCM decoders. We propose a pre-computation architecture incorporated with T-algorithm for VD, which can effectively reduce the power consumption without degrading the decoding speed much. A general solution to derive the optimal pre-computation steps is also given in the paper. Implementation result of a VD for a rate-3/4 convolutional code used in a TCM system shows that compared with the full trellis VD, the pre-computation architecture reduces the power consumption by as much as 70% without performance loss, while the degradation in clock speed is negligible.This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by IEEE and can be found at: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6257480. ©2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Keywords: Trellis coded modulation (TCM), Viterbi decoder, VLS