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MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS
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作者 Lulu FANG Jihua MA +1 位作者 Kunkun SONG Xin YANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1594-1608,共15页
For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflect... For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined. 展开更多
关键词 continued fractions product of partial quotients Hausdorff dimension
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Cover story: Neuromodulation Brings Sunshine to Diseased Brains
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《General Psychiatry》 CSCD 2024年第1期32-32,共1页
Various invasive and non-invasive brain modulation methods are widely used to regulate sensory,cognitive,and motor functions both within local and large brain networks.This special issue provides innovative studies to... Various invasive and non-invasive brain modulation methods are widely used to regulate sensory,cognitive,and motor functions both within local and large brain networks.This special issue provides innovative studies to optimize relevant methods and understand their neural mechanisms,paving the way for personalized neuromodulation of cognitive function.The cover of this issue uses the image of the four heavenly Kings in Chinese culture who are in charge of good weather.It compares the process of neuroregulation technology that integrates the principles of sound,light electricity or magnetism in treating the diseased brain,to the moment when these gods cast their spells to bring sunshine and peace to the human brain in the midst of lightning and thunder. 展开更多
关键词 SUNSHINE LIGHTNING rings
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Rising utilization of stable isotopes in tree rings for climate change and forest ecology
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作者 Ru Huang Chenxi Xu +3 位作者 Jussi Grießinger Xiaoyu Feng Haifeng Zhu Achim Bräuning 《Journal of Forestry Research》 SCIE EI CAS CSCD 2024年第1期103-116,共14页
Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive re... Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive review.This study includes a bibliometric analysis-based review to better understand research trends in tree ring stable isotope research.Overall,1475 publications were selected from the Web of Science Core Collection for 1974-2023.The findings are that:(1)numbers of annual publications and citations increased since 1974.From 1974 to 1980,there were around two relevant publications per year.However,from 2020 to 2022,this rose sharply to 109 publications per year.Likewise,average article citations were less than four per year before 1990,but were around four per article per year after 2000;(2)the major subjects using tree ring stable isotopes include forestry,geosciences,and environmental sciences,contributing to 42.5%of the total during 1974-2023;(3)the top three most productive institutions are the Chinese Academy of Sciences(423),the Swiss Federal Institute for Forest,Snow and Landscape Research(227),and the University of Arizona(204).These achievements result from strong collaborations;(4)review papers,for example,(Dawson et al.,Annu Rev Ecol Syst 33:507-559,2002)and(McCarroll and Loader,Quat Sci Rev 23:771-801,2004),are among the most cited,with more than 1000 citations;(5)tree ring stable isotope studies mainly focus on climatology and ecology,with atmospheric CO_(2) one of the most popular topics.Since 2010,precipitation and drought have received increasing attention.Based on this analysis,the research stages,key findings,debated issues,limitations and direc-tions for future research are summarized.This study serves as an important attempt to understand the progress on the use of stable isotopes in tree rings,providing scientific guid-ance for young researchers in this field. 展开更多
关键词 Tree rings Stable isotopes Web of Science BIBLIOMETRIC
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Rational and Continuous Measurement of Emotional-Fingerprint, Emotional-Quotient and Categorical vs Proportional Recognition of Facial Emotions with M.A.R.I.E., Second Half
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作者 Philippe Granato Shreekumar Vinekar +1 位作者 Jean-Pierre Van Gansberghe Raymond Bruyer 《Open Journal of Psychiatry》 2024年第4期400-450,共51页
Context: The advent of Artificial Intelligence (AI) requires modeling prior to its implementation in algorithms for most human skills. This observation requires us to have a detailed and precise understanding of the i... Context: The advent of Artificial Intelligence (AI) requires modeling prior to its implementation in algorithms for most human skills. This observation requires us to have a detailed and precise understanding of the interfaces of verbal and emotional communications. The progress of AI is significant on the verbal level but modest in terms of the recognition of facial emotions even if this functionality is one of the oldest in humans and is omnipresent in our daily lives. Dysfunction in the ability for facial emotional expressions is present in many brain pathologies encountered by psychiatrists, neurologists, psychotherapists, mental health professionals including social workers. It cannot be objectively verified and measured due to a lack of reliable tools that are valid and consistently sensitive. Indeed, the articles in the scientific literature dealing with Visual-Facial-Emotions-Recognition (ViFaEmRe), suffer from the absence of 1) consensual and rational tools for continuous quantified measurement, 2) operational concepts. We have invented a software that can use computer-morphing attempting to respond to these two obstacles. It is identified as the Method of Analysis and Research of the Integration of Emotions (M.A.R.I.E.). Our primary goal is to use M.A.R.I.E. to understand the physiology of ViFaEmRe in normal healthy subjects by standardizing the measurements. Then, it will allow us to focus on subjects manifesting abnormalities in this ability. Our second goal is to make our contribution to the progress of AI hoping to add the dimension of recognition of facial emotional expressions. Objective: To study: 1) categorical vs dimensional aspects of recognition of ViFaEmRe, 2) universality vs idiosyncrasy, 3) immediate vs ambivalent Emotional-Decision-Making, 4) the Emotional-Fingerprint of a face and 5) creation of population references data. Methods: M.A.R.I.E. enables the rational, quantified measurement of Emotional Visual Acuity (EVA) in an individual observer and a population aged 20 to 70 years. Meanwhile, it can measure the range and intensity of expressed emotions through three Face- Tests, quantify the performance of a sample of 204 observers with hypernormal measures of cognition, “thymia” (defined elsewhere), and low levels of anxiety, and perform analysis of the six primary emotions. Results: We have individualized the following continuous parameters: 1) “Emotional-Visual- Acuity”, 2) “Visual-Emotional-Feeling”, 3) “Emotional-Quotient”, 4) “Emotional-Decision-Making”, 5) “Emotional-Decision-Making Graph” or “Individual-Gun-Trigger”, 6) “Emotional-Fingerprint” or “Key-graph”, 7) “Emotional-Fingerprint-Graph”, 8) detecting “misunderstanding” and 9) detecting “error”. This allowed us a taxonomy with coding of the face-emotion pair. Each face has specific measurements and graphics. The EVA improves from ages of 20 to 55 years, then decreases. It does not depend on the sex of the observer, nor the face studied. In addition, 1% of people endowed with normal intelligence do not recognize emotions. The categorical dimension is a variable for everyone. The range and intensity of ViFaEmRe is idiosyncratic and not universally uniform. The recognition of emotions is purely categorical for a single individual. It is dimensional for a population sample. Conclusions: Firstly, M.A.R.I.E. has made possible to bring out new concepts and new continuous measurements variables. The comparison between healthy and abnormal individuals makes it possible to take into consideration the significance of this line of study. From now on, these new functional parameters will allow us to identify and name “emotional” disorders or illnesses which can give additional dimension to behavioral disorders in all pathologies that affect the brain. Secondly, the ViFaEmRe is idiosyncratic, categorical, and a function of the identity of the observer and of the observed face. These findings stack up against Artificial Intelligence, which cannot have a globalist or regionalist algorithm that can be programmed into a robot, nor can AI compete with human abilities and judgment in this domain. *Here “Emotional disorders” refers to disorders of emotional expressions and recognition. 展开更多
关键词 M.A.R.I.E. Universality Idiosyncrasy Measurement of Emotional quotient Emotional Fingerprint Emotional Decision-Making Limbic Lobe
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Effectivity and safety of trifocal intraocular lenses and capsular tension rings implantation for cataract patients with axial high myopia
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作者 Shan Hua Qiu-Xia Xie +1 位作者 Hu Wang Jing-Xiang Zhong 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2024年第3期499-508,共10页
●AIM:To assess effectivity and safety of trifocal intraocular lenses(IOLs)and capsular tension rings in treating cataract patients with axial high myopia.●METHODS:A prospective nonrandomized controlled clinical tria... ●AIM:To assess effectivity and safety of trifocal intraocular lenses(IOLs)and capsular tension rings in treating cataract patients with axial high myopia.●METHODS:A prospective nonrandomized controlled clinical trial was conducted.Totally 98 eyes(74 patients)who underwent femtosecond laser-assisted cataract surgery(FLACS)with trifocal IOLs were enrolled in the study and followed up for 2y after surgery:46 eyes(33 patients)with capsular tension ring implantation in the long axial lengths(AL)group(26<AL<29 mm)and 52 eyes(41 patients)in the normal AL group(22<AL<24.5 mm).Postoperative outcomes about effectivity and safety,including the subjective and objective visual quality,and postoperative complications were assessed.●RESULTS:Uncorrected distance visual acuity at 5 m and uncorrected intermediate visual acuity at 60 and 80 cm in the long AL group were significantly worse than those in the normal AL group at 3mo postoperatively(P<0.05).The differences in reading speed,spectacle independence and potential visual complaints between the two groups were not statistically significant(P>0.05).The dysfunctional lens index and total modulation transfer function(MTF)average height were similar between the two groups.The postoperative internal coma aberrations in the axial high myopia eyes were significantly higher than that in the normal AL group(P<0.05).The total satisfaction score in the long AL group(91.32±2.76)was slightly higher than that in the normal AL group(90.36±3.47),but there was no difference(P=0.136).A statistically negative correlation was found between corrected distance visual acuity(CDVA)and dysfunctional lens index(r=-0.382,P=0.009),and between CDVA and the total MTF average height(r=-0.374,P=0.01).But there was no significant correlation between CDVA and total satisfaction score(r=0.059,P=0.696).Postoperative complications mainly presented as posterior capsular opacity(PCO),retinal detachment and cystoid macular edema.There was no difference in the incidence of fundus disease(6.5%vs 3.8%,P=0.663)or PCO(17.4%vs 7.7%,P=0.217)between the two groups at two years.●CONCLUSION:The utilization of trifocal IOL and capsular tension ring implantation is beneficial for cataract patients with axial high myopia undergoing FLACS.This approach not only ensures excellent subjective feelings and objective visual quality,but also does not increase the incidence of postoperative complications. 展开更多
关键词 trifocal intraocular lenses capsular tension ring axial high myopia CATARACT visual quality
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Stability of neodymium:YAG laser posterior capsulotomy in eyes with capsular tension rings 被引量:1
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作者 Yang Kyung Cho Min Sun Kim 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2023年第6期891-896,共6页
·AIM: To evaluate the stability of neodymium(Nd):YAG laser posterior capsulotomy in eyes with capsular tension rings(CTRs).·METHODS: A total of 60 eyes that underwent cataract surgery and laser posterior cap... ·AIM: To evaluate the stability of neodymium(Nd):YAG laser posterior capsulotomy in eyes with capsular tension rings(CTRs).·METHODS: A total of 60 eyes that underwent cataract surgery and laser posterior capsulotomy postoperatively were included in this retrospective cohort study. To evaluate the safety and stability of capsulotomy, changes in the size of posterior capsulotomy and anterior chamber depth(ACD) in three groups: the group without CTR, the group with 12 mm CTRs, and the group with 13 mm CTRs, at 1wk, 3, 12, and 15mo after capsulotomy, were compared. ·RESULTS: In the group without CTR and the group with 12 mm CTR, there was no significant change in ACD at every post-laser follow-up. In the group with 13 mm CTR, the ACD change was significant until 3mo after capsulotomy. In all groups, there was a significant increase in the area of capsulotomy between 1wk and 3mo post-laser. Between 3 and 12mo post-laser, only the group with 13 mm CTR showed a significant increase in the area of capsulotomy(P<0.01). ·CONCLUSION: Laser posterior capsulotomy is safe in all three groups. The capsulotomy and ACD become stabilized and have not shown significant changes since 1y postlaser, even with larger CTRs. The maintenance of centrifugal capsular tension can last longer with larger CTRs, and the stability of the capsulotomy site can be reached about 12mo after capsulotomy in pseudophakic eyes with larger CTRs. 展开更多
关键词 Nd:YAG laser CAPSULOTOMY capsular tension ring
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A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD
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作者 纪正超 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2553-2572,共20页
In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one... In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one can get the long-time existence for the inverse curvature flow.Moreover,we also get that the principal curvatures of the evolving hypersurface converge to 1 when t→+∞. 展开更多
关键词 STAR-SHAPED quotient curvature support function
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β-Ga_(2)O_(3) junction barrier Schottky diode with NiO p-well floating field rings
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作者 何启鸣 郝伟兵 +6 位作者 李秋艳 韩照 贺松 刘琦 周选择 徐光伟 龙世兵 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期73-79,共7页
Recently,β-Ga_(2)O_(3),an ultra-wide bandgap semiconductor,has shown great potential to be used in power devices blessed with its unique material properties.For instance,the measured average critical field of the ver... Recently,β-Ga_(2)O_(3),an ultra-wide bandgap semiconductor,has shown great potential to be used in power devices blessed with its unique material properties.For instance,the measured average critical field of the vertical Schottky barrier diode(SBD)based onβ-Ga_(2)O_(3) has reached 5.45 MV/cm,and no device in any material has measured a greater before.However,the high electric field of theβ-Ga_(2)O_(3) SBD makes it challenging to manage the electric field distribution and leakage current.Here,we showβ-Ga_(2)O_(3) junction barrier Schottky diode with NiO p-well floating field rings(FFRs).For the central anode,we filled a circular trench array with NiO to reduce the surface field under the Schottky contact between them to reduce the leakage current of the device.For the anode edge,experimental results have demonstrated that the produced NiO/β-Ga_(2)O_(3) heterojunction FFRs enable the spreading of the depletion region,thereby mitigating the crowding effect of electric fields at the anode edge.Additionally,simulation results indicated that the p-NiO field plate structure designed at the edges of the rings and central anode can further reduce the electric field.This work verified the feasibility of the heterojunction FFRs inβ-Ga_(2)O_(3) devices based on the experimental findings and provided ideas for managing the electric field ofβ-Ga_(2)O_(3) SBD. 展开更多
关键词 gallium oxide Schottky barrier diode nickel oxide floating field rings
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AusMed Brings Game-Changing Healthcare Innovations from Hong Kong,China to the World——An interview with Christine Yip,Founder and CEO of AusMed Global Limited
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作者 Guo Yan 《China's Foreign Trade》 2023年第4期23-26,共4页
“As a non-invasive alternative to the traditional finger-prick blood ketone testing devices,boasting a high level of accuracy comparable to industrial gold standards typically attainable only through bulky and expens... “As a non-invasive alternative to the traditional finger-prick blood ketone testing devices,boasting a high level of accuracy comparable to industrial gold standards typically attainable only through bulky and expensive specialty equipment,we proudly introduce the world’s first-of-its-kind handheld breath ketone(BrAce)analyser,empowered by our patented disruptive photonic sensing technologies.These innovations are aimed at providing a more effective approach to managing diabetes and ketosis(fat metabolism),”said Christine Yip,founder and CEO of AusMed Global Limited,during a recent interview with China’s Foreign Trade magazine. 展开更多
关键词 KETONE rings typically
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Studying Tuff Rings and Volcanic Hazards in a Tropical Setting: The Case of the Batoke Tuff Ring, Limbe, SW Region Cameroon
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作者 George Teke Mafany Edison Forbuck Njei +6 位作者 Gerald G. J. Ernst Wilson Yetoh Fantong Cheo Emmanue Suh Samuel Ndonwi Ayonghe Robert Stephen John Sparks Koffi Teke Mafany Stephen Manga Njome 《Open Journal of Geology》 2023年第8期883-899,共17页
In subtropical volcanic environments, there are often few accessible outcrops. These are often highly weathered and of very poor quality. Soil development is rapid (1 cm/y) and small eruptions are unlikely to be prese... In subtropical volcanic environments, there are often few accessible outcrops. These are often highly weathered and of very poor quality. Soil development is rapid (1 cm/y) and small eruptions are unlikely to be preserved in the geological record. Reconstructing past eruptions and assessing hazards is a challenge. Here, we studied a poorly outcropping tuff ring (very poor, incomplete sections) with the best outcrop observed at a beach cliff (up to ca. 5 - 10 m high) at Batoke, to the south of Mt Cameroon volcano. Mt Cameroon has a few tuff rings, currently of unknown ages, near the SW coast of Cameroon. In the Batoke case, the sequence is dominated by gently dipping tuff beds varying in the proportion of lithics, juvenile clasts, and accretionary lapilli (acc-laps). Several beds are close-packed with acc-laps of up to 10 - 15 mm diameter. Part of the section is gullied by mud flow deposits. The rocks are highly weathered but differential weathering enhances relationships. Quantitative data can be extracted from a detailed study of outcrops’ external surfaces. The preserved section is close to where the deposits were initially thickest and where acc-laps were most abundant and largest. There is an empirical correlation between maximum acc-lap size in the thickest outcrop and eruption column height. This and the deposit features suggest that the Batoke eruption was pulsating but dominated by fallout, with a water and ice-rich eruption column reaching 10 - 15 km high. Recycling of water drops and ice-coated fine ash accumulated during eruption. At switch off, wholesale gravitational collapse of this material produced the mud flows, which gullied the previously-laid down deposits. Such ash fall and mud flows can represent a substantial hazard, e.g. they can gully down through towns and roads and cut evacuation routes. This study illustrates how, at subtropical tuff rings, it is possible to extract key data needed for hazard assessment from only 1 - 2 poor outcrops. 展开更多
关键词 Batoke Tuff Ring (BTR) Accretionary Lapilli
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Brain metabolic profile assessed by magnetic resonance spectroscopy in children with Down syndrome:Relation to intelligence quotient
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作者 Nesreen Safwat El Feil Heba S Elmahdy +3 位作者 Rasha Ahmed Elmahdy Ahmed Abd-Elbasset Aboelezz Heba S Dawoud Mohammed Al-Beltagi 《World Journal of Clinical Pediatrics》 2023年第5期310-318,共9页
BACKGROUND Down syndrome(DS)is one of the most common causes of intellectual disability.Children with DS have varying intelligence quotient(IQ)that can predict their learning abilities.AIM To assess the brain metaboli... BACKGROUND Down syndrome(DS)is one of the most common causes of intellectual disability.Children with DS have varying intelligence quotient(IQ)that can predict their learning abilities.AIM To assess the brain metabolic profiles of children with DS and compare them to standard controls,using magnetic resonance spectroscopy(MRS)and correlating the results with IQ.METHODS This case-control study included 40 children with DS aged 6-15 years and 40 age and sex-matched healthy children as controls.MRS was used to evaluate ratios of choline/creatine(Cho/Cr),N-acetyl aspartic acid/creatine(NAA/Cr),and myoinositol/creatine(MI/Cr(in the frontal,temporal,and occipital lobes and basal ganglia and compared to controls and correlated with IQ.RESULTS Children with DS showed significant reductions in NAA/Cr and MI/Cr and a non-significant reduction in Cho/Cr in frontal lobes compared to controls.Additionally,we observed significant decreases in NAA/Cr,MI/Cr,and Cho/Cr in the temporal and occipital lobes and basal ganglia in children with DS compared to controls.Furthermore,there was a significant correlation between IQ and metabolic ratios in the brains of children with DS.CONCLUSION Brain metabolic profile could be a good predictor of IQ in children with DS. 展开更多
关键词 CHILDREN Down syndrome Magnetic resonance spectroscopy Metabolic profile Intelligence quotient
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Relative Ding Projective Modules over Formal Triangular Matrix Rings
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作者 Hongyan Fan Xi Tang 《Journal of Applied Mathematics and Physics》 2023年第6期1598-1614,共17页
Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t... Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module. 展开更多
关键词 Formal Triangular Matrix Ring Relative Ding Projective Module Relative Ding Projective Dimension
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Penile and scrotal strangulation by stainless steel rings in an human immunodeficiency virus positive man: A case report
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作者 Daisuke Usuda Nobuyoshi Kaminishi +22 位作者 Masashi Kato Yuto Sugawara Runa Shimizu Tomotari Inami Shiho Tsuge Riki Sakurai Kenji Kawai Shun Matsubara Risa Tanaka Makoto Suzuki Shintaro Shimozawa Yuta Hotchi Ippei Osugi Risa Katou Sakurako Ito Kentaro Mishima Akihiko Kondo Keiko Mizuno Hiroki Takami Takayuki Komatsu Jiro Oba Tomohisa Nomura Manabu Sugita 《World Journal of Clinical Cases》 SCIE 2023年第24期5811-5816,共6页
BACKGROUND Penoscrotal constriction devices are either used as autoerotic stimuli or to increase sexual pleasure or performance by maintaining an erection for a longer period,and a variety of metallic and non-metallic... BACKGROUND Penoscrotal constriction devices are either used as autoerotic stimuli or to increase sexual pleasure or performance by maintaining an erection for a longer period,and a variety of metallic and non-metallic objects are used.On the other hand,penile strangulation is a rare urologic emergency that requires prompt evaluation and intervention to prevent long-term complications.The goal of treating penile incarceration is to remove the foreign object as soon as possible.On the other hand,removal can be very challenging,and often requires resourcefulness and a multidisciplinary approach.CASE SUMMARY A 47-year-old man who has sex with men was transferred to our hospital for persistent phallodynia and scrotal pain,accompanying swelling due to strangulation by stainless steel rings.His medical history included acquired immunodeficiency syndrome.One day prior,he had put three stainless steel rings on his penis and scrotum before sexual intercourse.After sexual intercourse,he was unable to remove them,due to swelling of his penis and scrotum.The swelling persisted,and he felt pain in the affected area the next day,then he was transferred to our hospital by ambulance.The emergency department found that his penis and scrotum were markedly engorged and swollen.We established a diagnosis of penile and scrotal strangulation by stainless steel rings.We unsuccessfully attempted to cut the rings using a cutter,then requested a rescue team via emergency medical service.They cut through each ring in two places,using an electric-powered angle grinder,and successfully removed all of the pieces.Finally,he was discharged and went home.CONCLUSION We report the first case of penile and scrotal strangulation by stainless steel rings in an human immunodeficiency virus positive person. 展开更多
关键词 Penile strangulation Stainless steel ring Human immunodeficiency virus Urologic emergency Management Case report
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Diophantine Quotients and Remainders with Applications to Fermat and Pythagorean Equations
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作者 Prosper Kouadio Kimou François Emmanuel Tanoé 《American Journal of Computational Mathematics》 2023年第1期199-210,共12页
Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pyth... Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pythagoras’- Fermat’s equation defined as follows.                                                                                         (1) when , it is well known that this equation has an infinity of solutions but has none (non-trivial) when . We also know that the last result, named Fermat-Wiles theorem (or FLT) was obtained at great expense and its understanding remains out of reach even for a good fringe of professional mathematicians. The aim of this research is to set up new simple but effective tools in the treatment of Diophantine equations and that of Pythagoras-Fermat. The tools put forward in this research are the properties of the quotients and the Diophantine remainders which we define as follows. Let a non-trivial triplet () solution of Equation (1) such that . and are called the Diophantine quotients and remainders of solution . We compute the remainder and the quotient of b and c by a using the division algorithm. Hence, we have: and et with . We prove the following important results. if and only if and if and only if . Also, we deduce that or for any hypothetical solution . We illustrate these results by effectively computing the Diophantine quotients and remainders in the case of Pythagorean triplets using a Python program. In the end, we apply the previous properties to directly prove a partial result of FLT. . 展开更多
关键词 Diophantine Equation Modular Arithmetic Fermat-Wiles Theorem Pythagorean Triplets Division Theorem Division Algorithm Python Program Diophantine quotients Diophantine Remainders
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An Introduction to the Theory of Matrix Near-Rings
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作者 Saviour Chibeti Iness Kyapwanyama 《Advances in Pure Mathematics》 2023年第2期71-95,共25页
Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive ... Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive laws does not hold in general. We introduce two ways in which matrix near-rings can be defined and discuss the structure of each. One is as given by Beildeman and the other is as defined by Meldrum. Beildeman defined his matrix near-rings as normal arrays under the operation of matrix multiplication and addition. He showed that we have a matrix near-ring over a near-ring if, and only if, it is a ring. In this case it is not possible to obtain a matrix near-ring from a proper near-ring. Later, in 1986, Meldrum and van der Walt defined matrix near-rings over a near-ring as mappings from the direct sum of n copies of the additive group of the near-ring to itself. In this case it can be shown that a proper near-ring is obtained. We prove several properties, introduce some special matrices and show that a matrix notation can be introduced to make calculations easier, provided that n is small. 展开更多
关键词 NEAR-rings First Near-Ring Isomorphism Zero Symmetric Near-Ring Near-Ring Module and Matrix Near-rings
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比较优势视角下我国虚拟水流动归因分析
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作者 何国华 赵勇 +3 位作者 秦长海 李溦 姜珊 李雯晴 《南水北调与水利科技(中英文)》 CAS CSCD 北大核心 2024年第1期1-11,共11页
虚拟水是近年来水资源领域的研究热点,而相关研究成果主要集中于虚拟水转移的规模核算及其特征分析,对虚拟水转移的动力成因较少讨论,所以借助比较优势理论中的区位商、增长商指数,量化解析农林牧渔、工业、建筑业、批发零售、交通运输... 虚拟水是近年来水资源领域的研究热点,而相关研究成果主要集中于虚拟水转移的规模核算及其特征分析,对虚拟水转移的动力成因较少讨论,所以借助比较优势理论中的区位商、增长商指数,量化解析农林牧渔、工业、建筑业、批发零售、交通运输、住宿餐饮、金融、房地产、其他服务业9大行业的发展优势及增长潜力,并分析这9大行业虚拟水流动格局与行业比较优势的相关关系。研究结果表明:各行业虚拟水流动格局与行业比较优势具有明显关联,2002—2017年间我国72%的虚拟水会从具有比较优势的地区向不具备优势的地区转移,71%的虚拟水转移量会受到行业发展速度影响。研究成果预期可为我国水资源宏观管理及节水政策制定提供理论依据及决策参考。决策参考。 展开更多
关键词 虚拟水战略 行业比较优势 相关性 增长商 区位商
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基于PTFE矩形密封圈的高压容器密封结构设计 被引量:2
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作者 鲁寨军 孙永龙 钟睦 《润滑与密封》 CAS CSCD 北大核心 2024年第4期95-102,共8页
PTFE矩形密封圈具有耐化学性能好、截面稳定性高等优点,可以有效解决腐蚀性介质的密封问题。但在实际使用中,PTFE矩形密封圈及其适配沟槽的尺寸设计缺乏参考依据。针对上述问题,根据高压容器端面密封结构的形状与受力特征,在Ansys Workb... PTFE矩形密封圈具有耐化学性能好、截面稳定性高等优点,可以有效解决腐蚀性介质的密封问题。但在实际使用中,PTFE矩形密封圈及其适配沟槽的尺寸设计缺乏参考依据。针对上述问题,根据高压容器端面密封结构的形状与受力特征,在Ansys Workbench中建立PTFE矩形密封圈的二维轴对称模型,采用双线性等向强化模型表征PTFE的力学性能,对基于PTFE矩形密封圈的高压容器端面密封结构进行分析和设计,讨论压缩率、PTFE矩形密封圈几何参数和沟槽结构参数对高压容器端面密封性能的影响。结果表明,压缩率、矩形圈的高度和宽度以及矩形圈与沟槽侧壁的间隙对密封性能的影响较大,而内径对密封性能的影响较小,因而设计时应优先考虑沟槽深度、矩形圈的截面尺寸以及与沟槽的装配位置等参数。确定PTFE矩形密封圈及适配沟槽的尺寸后,采用有限元仿真手段验证了设计的密封结构在常温30 MPa高压下的密封性能,证实了设计的合理性。 展开更多
关键词 PTFE矩形密封圈 高压容器 密封结构 密封性能
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吉西他滨联合顺铂方案治疗复发性三阴性乳腺癌的疗效观察 被引量:1
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作者 申鹏 刘正义 +2 位作者 闫园 于博凡 于洋 《中国合理用药探索》 CAS 2024年第2期62-68,共7页
目的:探究吉西他滨联合顺铂方案在蒽环、紫杉类药物治疗后复发性三阴性乳腺癌(TNBC)患者中的应用效果。方法:选取2019年1月~2021年1月期间某院收治的81例蒽环、紫杉类药物治疗后复发性TNBC患者作为研究对象,采用随机、单盲试验研究方法... 目的:探究吉西他滨联合顺铂方案在蒽环、紫杉类药物治疗后复发性三阴性乳腺癌(TNBC)患者中的应用效果。方法:选取2019年1月~2021年1月期间某院收治的81例蒽环、紫杉类药物治疗后复发性TNBC患者作为研究对象,采用随机、单盲试验研究方法,依据随机数字表法分为A组(n=40)和B组(n=41)。A组患者给予注射用盐酸吉西他滨联合卡培他滨片治疗,B组患者给予注射用盐酸吉西他滨联合注射用顺铂治疗。比较两组临床疗效、血清肿瘤标志物[癌胚抗原(CEA)、糖类抗原153(CA153)、糖类抗原125(CA125)]水平变化、生活质量情况[欧洲癌症研究与治疗组织生命质量量表(EORTC QLQ-C30)]、不良反应发生情况及治疗后2年内患者的预后情况。结果:治疗后,B组治疗总有效率(82.93%)高于A组(60.00%,P<0.05)。两组血清CEA、CA153、CA125水平均降低(P<0.05),且B组低于A组(P<0.05)。两组EORTC QLQ-C30评分在疲劳、失眠方面均降低(P<0.05),且B组低于A组(P<0.05);两组EORTC QLQ-C30评分在总体健康方面均升高(P<0.05),且B组高于A组(P<0.05);两组EORTC QLQ-C30评分在恶心呕吐、食欲丧失、便秘方面比较无统计学差异(P>0.05)。两组患者治疗期间不良反应总发生率比较无统计学差异(P>0.05)。B组患者2年内复发率(14.63%)低于A组(40.00%,P<0.05),中位无进展生存期[(6.65±1.45)个月]长于A组[(4.26±1.23)个月,P<0.05],稳定病例数(58.54%)高于A组(30.00%,P<0.05)。结论:与吉西他滨联合卡培他滨相比,吉西他滨联合顺铂治疗方案在蒽环、紫杉类药物治疗后复发性TNBC患者中临床疗效更佳,可有效降低患者血清肿瘤标志物水平,提高生活质量,改善预后。 展开更多
关键词 吉西他滨 顺铂 蒽环 紫杉类药物 三阴性乳腺癌 复发
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*-诣零McCoy环
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作者 王尧 李欣 任艳丽 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2024年第2期162-171,共10页
研究了具有对合映射*-诣零McCoy环的性质,给出了一批*-诣零McCoy环例子,并讨论了其扩张和*-斜多项式环的*-诣零McCoy性,证明了(1)设*-环R满足nil(R[x])=nil(R)[x],则环R是*-诣零McCoy环当且仅当环R[x]是*-诣零McCoy环;(2)设R[x;*]是*-... 研究了具有对合映射*-诣零McCoy环的性质,给出了一批*-诣零McCoy环例子,并讨论了其扩张和*-斜多项式环的*-诣零McCoy性,证明了(1)设*-环R满足nil(R[x])=nil(R)[x],则环R是*-诣零McCoy环当且仅当环R[x]是*-诣零McCoy环;(2)设R[x;*]是*-斜多项式环,如果R是*-可逆环,则R[x;*]是*-诣零McCoy环。 展开更多
关键词 对合 McCoy环 *-诣零McCoy环 *-斜多项式环
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汉语发展性阅读障碍评估测验的编制及效度和信度检验
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作者 孟祥芝 黎程正家 《中国心理卫生杂志》 CSCD 北大核心 2024年第8期706-712,共7页
目的:编制汉语发展性阅读障碍评估测验(C-DDAT),并进行效度和信度检验。方法:根据美国精神障碍诊断与统计手册第5版(DSM-5)关于阅读障碍核心特征描述以及阅读理论编制汉语发展性阅读障碍评估测验,包含汉字阅读准确性、流畅性以及阅读理... 目的:编制汉语发展性阅读障碍评估测验(C-DDAT),并进行效度和信度检验。方法:根据美国精神障碍诊断与统计手册第5版(DSM-5)关于阅读障碍核心特征描述以及阅读理论编制汉语发展性阅读障碍评估测验,包含汉字阅读准确性、流畅性以及阅读理解3个因子。在1925名1~6年级儿童中检验结构效度、内部一致性信度、复本信度,在63名典型发展儿童和26名发展性阅读障碍儿童中检验重测信度。结果:三因子结构模型拟合良好(χ^(2)/df=5.91,CFI=0.996,TLI=0.992,SRMR=0.014,RMSEA=0.056)。效标关联效度为0.51~0.98。汉字阅读准确性测验的内部一致性信度为0.99,汉字阅读流畅性和汉字阅读准确性的复本信度分别为0.94和0.98,重测信度为0.73~0.98。对临床样本进行ROC曲线分析发现,阅读商数(阅读测验综合评分)的区分灵敏性和特异性分别为0.92和0.98。结论:汉语发展性阅读障碍评估测验的效度、信度达到心理测量学要求,可用于基础研究中对儿童基本阅读技能的评估以及临床实践中对儿童阅读障碍诊断的参考。 展开更多
关键词 阅读障碍 评估测验 阅读商数 效度 信度
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