Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant s...Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.展开更多
Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stre...Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources： force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.展开更多
In the process of eliminating variables in a symbolic polynomial system,the extraneous factors are referred to the unwanted parameters of resulting polynomial.This paper aims at reducing the number of these factors vi...In the process of eliminating variables in a symbolic polynomial system,the extraneous factors are referred to the unwanted parameters of resulting polynomial.This paper aims at reducing the number of these factors via optimizing the size of Dixon matrix.An optimal configuration of Dixon matrix would lead to the enhancement of the process of computing the resultant which uses for solving polynomial systems.To do so,an optimization algorithm along with a number of new polynomials is introduced to replace the polynomials and implement a complexity analysis.Moreover,the monomial multipliers are optimally positioned to multiply each of the polynomials.Furthermore,through practical implementation and considering standard and mechanical examples the efficiency of the method is evaluated.展开更多
The total transverse forces on each of the two piles in the side-by-side arrangement and tandem arrangement are experimentally investigated in irregular waves and the total in-line wave forces are measured simultaneou...The total transverse forces on each of the two piles in the side-by-side arrangement and tandem arrangement are experimentally investigated in irregular waves and the total in-line wave forces are measured simultaneously. The statistical and spectral characteristics of the transverse forces are analyzed. The ratio of the transverse force on each pile in group to that on a single pile is defined as the transverse groupling-pile factor, KGL. Both the transverse coefficients CLG and KGL for each pile in array are varied with the relative pile distance and KC number and their relationships are presented in this paper. Also the ratio of the resultant wave froce of in-line force and transverse force to the in-line force and the vriation of the resultant coefficient are investigated.展开更多
Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related...Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and "production" of the gradient-information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.展开更多
The simulated unified resultant amplitude theory studies function and polar graphs of sinusoidal radial waves including the cosine, sine, and summation waves for determining separate combination-wave equations arising...The simulated unified resultant amplitude theory studies function and polar graphs of sinusoidal radial waves including the cosine, sine, and summation waves for determining separate combination-wave equations arising from 2D spatial oscillator fields in each of the four quadrants corresponding to the x-y Cartesian reference frame. Combination-wave fluctuations in terms of their algebraic signs are then extrapolated and mathematically modeled relative to the quadrant number by way of Euler’s equation. The resulting sign fluctuation equations are used to synthesize the combination-wave equations into a single unified equation along with a unified wave rotation solution that adequately represents all four quadrant-specific wave equations. Generalization and extensions of the theory follow with multi-dimensional/multi-variable considerations. Subsequently, utilization of the theory regarding an applied mathematics and physics-based kinematics motion problem, a generalized differential equation solution for a spring system, as well as a four-dimensional/four-variable dual-cone example are provided for validating the methodology. Consequently, it is shown that the proposed unified model is useful for performing a compact resultant amplitude analysis within general applications involving various wave phenomena.展开更多
The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the orde...The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the order of magnitude of ex(n,H)for bipartite graphs is known only in a handful of cases.In particular,giving explicit constructions of extremal graphs is very challenging in this field.In this paper,we develop a polynomial resultant approach to the algebraic construction of explicit extremal graphs,which can efficiently decide whether a specified structure exists.A key insight in our approach is the multipolynomial resultant,which is a fundamental tool of computational algebraic geometry.Our main results include the matched lower bounds on the Turán number of 1-subdivision of K3,t1and the linear Turán number of the Berge theta hypergraph■_(3,t_(2))^(B).where t_(1)=25 and t_(2)=217.Moreover,the constant t1improves the random algebraic construction of Bukh and Conlon(2018)and makes the known estimation better on the smallest value of t1concerning a problem posed by Conlon et al.(2021)by reducing the value from a magnitude of 10^(56)to the number 25,while the constant t_(2)improves a result of He and Tait(2019).展开更多
In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm i...In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm is a very efficient algorithm,but which deals with the case of three polynomial equations with two variables at most.In this paper,we extend the algorithm to the general case of n+1 polynomial equations in nvariables.The algorithm has been implemented in Maple 9.By testing the random polyno mial equations,the results demonstrate that the efficiency of our program is much better than the previous methods,and it is exciting that the necessary condition for the existence of common intersection points on four general surfaces in which the degree with respect to every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by our program.展开更多
It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the auth...It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.展开更多
Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational...Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.展开更多
In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the ...In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.展开更多
Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very diff...Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively.展开更多
Objective:To investigate the long-term prognosis and postoperative cosmetic outcomes of breast-conserving surgery combined with sentinel lymph node biopsy in patients with early-stage breast cancer,providing a referen...Objective:To investigate the long-term prognosis and postoperative cosmetic outcomes of breast-conserving surgery combined with sentinel lymph node biopsy in patients with early-stage breast cancer,providing a reference for the selection of clinical treatment plans.Methods:A retrospective analysis was conducted on the clinical data of 68 patients with early-stage breast cancer admitted from January 2022 to December 2025.Based on the surgical approach,patients were divided into an observation group(breast-conserving surgery+sentinel lymph node biopsy)and a control group(other surgical methods such as modified radical mastectomy/total mastectomy).Clinical and pathological characteristics,incidence of postoperative complications,follow-up prognosis,and satisfaction with cosmetic outcomes were compared between the two groups.Results:Among the 68 patients,41 were in the observation group and 27 in the control group.The average age of patients in the observation group was(54.32±8.15)years,while that in the control group was(62.45±9.76)years.The average tumor size in the observation group was(1.86±0.72)cm,compared to(3.21±1.45)cm in the control group.The incidence of postoperative complications in the observation group was 9.76%,significantly lower than that in the control group at 33.33%(P<0.05).The 6-month disease-free survival rate was 95.12%in the observation group and 88.89%in the control group,with no statistically significant difference between the two groups(P>0.05).The excellent and good rate of cosmetic outcomes in the observation group was 87.80%,significantly higher than that in the control group at 29.63%(P<0.05).Conclusion:Breast-conserving surgery combined with sentinel lymph node biopsy for early-stage breast cancer can achieve long-term prognostic outcomes comparable to those of traditional radical surgery,with the advantages of fewer postoperative complications and superior cosmetic results.This approach is worthy of clinical promotion and application,particularly for early-stage breast cancer patients who have a demand for preserving breast morphology.展开更多
The original online version of this article was revised:Several errors occurred in the published version of the article.These have now been corrected as follows:Page 2,section"2.2 Laser Texturing Procedure of Sur...The original online version of this article was revised:Several errors occurred in the published version of the article.These have now been corrected as follows:Page 2,section"2.2 Laser Texturing Procedure of Surfaces",line 2:The device name was corrected from"YDFLP-E-50-M8"to"YDFLP-50-M8."Page 3,Section 2.4:The phrase"95%confidence interval"has been corrected to"95%confidence level."Page 3,Figure 1 caption:The phrase"fandg"has been corrected to"f and g."The order"C4 and C12"has been reversed to"C12 and C4,"in accordance with the display order in the figure.Page 4,Figure reference:The phrase"Figs.4c and d"has been corrected to"Figs.5b and c."Page 5,paragraph starting with"The ANOVA results are presented...":The phrase"95%confidence interval"has been corrected to"95%confidence level."展开更多
I offer suggestions to increase the probability of success of an international research project.Collaborative studies often produce more innovative and transformative scientific results than work done by a single inve...I offer suggestions to increase the probability of success of an international research project.Collaborative studies often produce more innovative and transformative scientific results than work done by a single investigator or an isolated team.My advice is intended for early-career scientists.The product of the collaboration may be high-impact research publications,enhanced geophysical monitoring capabilities in a foreign country,or an advanced training course.Choosing the right international partner is the most important step.Keeping an open mind and being receptive to suggestions to modify the initial concept is critical.Other key steps include having a mutually agreed upon plan with achievable goals and well-defined expected outcomes.International cooperation is a richly rewarding experience that accelerates progress in the Earth Sciences.展开更多
BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram ...BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram using internal and external validation to predict survival in patients with ampullary adenocarcinoma.METHODS Data were sourced from the surveillance,epidemiology,and end results stat database.The patients in the database were randomized in a 7:3 ratio into training and validation groups.Using Cox regression univariate and multivariate analyses in the training group,we identified independent risk factors for overall survival and cancer-specific survival to develop the nomogram.The nomogram was validated with a cohort of patients from the First Affiliated Hospital of the Army Medical University.RESULTS For overall and cancer-specific survival,12(sex,age,race,lymph node ratio,tumor size,chemotherapy,surgical modality,T stage,tumor differentiation,brain metastasis,lung metastasis,and extension)and 6(age;surveillance,epidemiology,and end results stage;lymph node ratio;chemotherapy;surgical modality;and tumor differentiation)independent risk factors,respectively,were incorporated into the nomogram.The area under the curve values at 1,3,and 5 years,respectively,were 0.807,0.842,and 0.826 for overall survival and 0.816,0.835,and 0.841 for cancer-specific survival.The internal and external validation cohorts indicated good consistency of the nomogram.CONCLUSION The dynamic nomogram offers robust predictive efficacy for the overall and cancer-specific survival of ampullary adenocarcinoma.展开更多
Journal of Future Foods(ISSN 2772-5669.Owner:Bejjing Academy of Food Sciences.Production and Hosting:Elsevier B.V.on bchalf of KcAi Communications Co,Ltd.)is an intecrnational,pcer-reviewed open access journal bclongi...Journal of Future Foods(ISSN 2772-5669.Owner:Bejjing Academy of Food Sciences.Production and Hosting:Elsevier B.V.on bchalf of KcAi Communications Co,Ltd.)is an intecrnational,pcer-reviewed open access journal bclonging to the disciplinc of food scicnce and technology.The aim of the journal is to report latcst rescarch results of high-tcch in food science.We welcome submissions that drive the ficld of food science towards whole food nutrition,intelligencc and high technology.展开更多
Retrieval analysis in total knee arthroplasty(TKA)has been little studied in the literature.A narrative review of the literature to understand the current importance of retrieval analysis in TKA has been conducted.On ...Retrieval analysis in total knee arthroplasty(TKA)has been little studied in the literature.A narrative review of the literature to understand the current importance of retrieval analysis in TKA has been conducted.On August 27,2024,a literature search was performed in PubMed using“TKA retrieval analysis”as keywords.A total of 160 articles were found,of which only 19 were analyzed because they were directly related to the subject of this article.Rotating-platform(mobile-bearing)TKA has no surface damage advantage over fixed-bearing TKA.TKAs with central locking mechanisms are more prone to debond from the cement mantle.No major wear of the polyethylene(PE)component in TKA using oxidized zirconium components occurs.Femoral components of cobalt-chromium roughen more than oxidized zirconium femoral components.The use of a polished tibial tray over an unpolished design is advised.At short-run assessment(15 months on average),antioxidant-stabilized highly crosslinked PE components are not clinically different in surface damage,density of crosslinking,or oxidation compared to standard remelted highly crosslinked PE components.A correlation between implant position and PE component surface damage has been reported.It shows the importance of optimizing component position to reduce PE component damage.Contemporary knee tumor megaendoprostheses show notable volumetric metal wear originated at the rotating hinge.Retrieval analysis in TKA renders relevant data on how different prosthetic designs described in the literature perform.Such information can help to improve future prosthetic designs to increase prosthetic survival.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10172075)the Yu-Ying Foundation of Hunan University.
文摘Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.
基金Project supported by the National Natural Science Foundation of China (No.10472102)Special Foundation of City University of HongKong (No.9610022)Outstanding Young Teacher Foundation of Hunan Province (No.521105236)the Yu-Ying Foundation of Hunan University (No.531103011110)
文摘Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources： force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.
文摘In the process of eliminating variables in a symbolic polynomial system,the extraneous factors are referred to the unwanted parameters of resulting polynomial.This paper aims at reducing the number of these factors via optimizing the size of Dixon matrix.An optimal configuration of Dixon matrix would lead to the enhancement of the process of computing the resultant which uses for solving polynomial systems.To do so,an optimization algorithm along with a number of new polynomials is introduced to replace the polynomials and implement a complexity analysis.Moreover,the monomial multipliers are optimally positioned to multiply each of the polynomials.Furthermore,through practical implementation and considering standard and mechanical examples the efficiency of the method is evaluated.
文摘The total transverse forces on each of the two piles in the side-by-side arrangement and tandem arrangement are experimentally investigated in irregular waves and the total in-line wave forces are measured simultaneously. The statistical and spectral characteristics of the transverse forces are analyzed. The ratio of the transverse force on each pile in group to that on a single pile is defined as the transverse groupling-pile factor, KGL. Both the transverse coefficients CLG and KGL for each pile in array are varied with the relative pile distance and KC number and their relationships are presented in this paper. Also the ratio of the resultant wave froce of in-line force and transverse force to the in-line force and the vriation of the resultant coefficient are investigated.
文摘Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and "production" of the gradient-information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.
文摘The simulated unified resultant amplitude theory studies function and polar graphs of sinusoidal radial waves including the cosine, sine, and summation waves for determining separate combination-wave equations arising from 2D spatial oscillator fields in each of the four quadrants corresponding to the x-y Cartesian reference frame. Combination-wave fluctuations in terms of their algebraic signs are then extrapolated and mathematically modeled relative to the quadrant number by way of Euler’s equation. The resulting sign fluctuation equations are used to synthesize the combination-wave equations into a single unified equation along with a unified wave rotation solution that adequately represents all four quadrant-specific wave equations. Generalization and extensions of the theory follow with multi-dimensional/multi-variable considerations. Subsequently, utilization of the theory regarding an applied mathematics and physics-based kinematics motion problem, a generalized differential equation solution for a spring system, as well as a four-dimensional/four-variable dual-cone example are provided for validating the methodology. Consequently, it is shown that the proposed unified model is useful for performing a compact resultant amplitude analysis within general applications involving various wave phenomena.
基金supported by the Institute for Basic Science(IBS-R029-C4)supported by the National Key Research and Development Program of China(Grant No.2020YFA0712100)+1 种基金National Natural Science Foundation of China(Grant No.12231014)Beijing Scholars Program。
文摘The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the order of magnitude of ex(n,H)for bipartite graphs is known only in a handful of cases.In particular,giving explicit constructions of extremal graphs is very challenging in this field.In this paper,we develop a polynomial resultant approach to the algebraic construction of explicit extremal graphs,which can efficiently decide whether a specified structure exists.A key insight in our approach is the multipolynomial resultant,which is a fundamental tool of computational algebraic geometry.Our main results include the matched lower bounds on the Turán number of 1-subdivision of K3,t1and the linear Turán number of the Berge theta hypergraph■_(3,t_(2))^(B).where t_(1)=25 and t_(2)=217.Moreover,the constant t1improves the random algebraic construction of Bukh and Conlon(2018)and makes the known estimation better on the smallest value of t1concerning a problem posed by Conlon et al.(2021)by reducing the value from a magnitude of 10^(56)to the number 25,while the constant t_(2)improves a result of He and Tait(2019).
基金partially supported by the China NKBRSF Project(Grant No.2004CB318003)the"Hundreds Talents Plan"of Institute of Computing Technology,Chinese Academy of Sciences(20044040)
文摘In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm is a very efficient algorithm,but which deals with the case of three polynomial equations with two variables at most.In this paper,we extend the algorithm to the general case of n+1 polynomial equations in nvariables.The algorithm has been implemented in Maple 9.By testing the random polyno mial equations,the results demonstrate that the efficiency of our program is much better than the previous methods,and it is exciting that the necessary condition for the existence of common intersection points on four general surfaces in which the degree with respect to every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by our program.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11471209,61321064 and 61361136002the Innovation Program of Shanghai Municipal Education Commission under Grant No.14ZZ046
文摘It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.
基金supported by the Natural Science Foundation of China under Grant No. 10901163the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.
文摘In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.
基金supported by the National Key Basic Special Funds of China (Grant No. 2004CB318003)the Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KJCX2-YW-S02)+2 种基金the National Natural Science Foundation of China (Grant No. 90718041)Shanghai Leading Academic Discipline Project(Grant No. B412)the Doctor Startup Foundation of East China Normal University (Grant No. 790013J4)
文摘Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively.
文摘Objective:To investigate the long-term prognosis and postoperative cosmetic outcomes of breast-conserving surgery combined with sentinel lymph node biopsy in patients with early-stage breast cancer,providing a reference for the selection of clinical treatment plans.Methods:A retrospective analysis was conducted on the clinical data of 68 patients with early-stage breast cancer admitted from January 2022 to December 2025.Based on the surgical approach,patients were divided into an observation group(breast-conserving surgery+sentinel lymph node biopsy)and a control group(other surgical methods such as modified radical mastectomy/total mastectomy).Clinical and pathological characteristics,incidence of postoperative complications,follow-up prognosis,and satisfaction with cosmetic outcomes were compared between the two groups.Results:Among the 68 patients,41 were in the observation group and 27 in the control group.The average age of patients in the observation group was(54.32±8.15)years,while that in the control group was(62.45±9.76)years.The average tumor size in the observation group was(1.86±0.72)cm,compared to(3.21±1.45)cm in the control group.The incidence of postoperative complications in the observation group was 9.76%,significantly lower than that in the control group at 33.33%(P<0.05).The 6-month disease-free survival rate was 95.12%in the observation group and 88.89%in the control group,with no statistically significant difference between the two groups(P>0.05).The excellent and good rate of cosmetic outcomes in the observation group was 87.80%,significantly higher than that in the control group at 29.63%(P<0.05).Conclusion:Breast-conserving surgery combined with sentinel lymph node biopsy for early-stage breast cancer can achieve long-term prognostic outcomes comparable to those of traditional radical surgery,with the advantages of fewer postoperative complications and superior cosmetic results.This approach is worthy of clinical promotion and application,particularly for early-stage breast cancer patients who have a demand for preserving breast morphology.
文摘The original online version of this article was revised:Several errors occurred in the published version of the article.These have now been corrected as follows:Page 2,section"2.2 Laser Texturing Procedure of Surfaces",line 2:The device name was corrected from"YDFLP-E-50-M8"to"YDFLP-50-M8."Page 3,Section 2.4:The phrase"95%confidence interval"has been corrected to"95%confidence level."Page 3,Figure 1 caption:The phrase"fandg"has been corrected to"f and g."The order"C4 and C12"has been reversed to"C12 and C4,"in accordance with the display order in the figure.Page 4,Figure reference:The phrase"Figs.4c and d"has been corrected to"Figs.5b and c."Page 5,paragraph starting with"The ANOVA results are presented...":The phrase"95%confidence interval"has been corrected to"95%confidence level."
文摘I offer suggestions to increase the probability of success of an international research project.Collaborative studies often produce more innovative and transformative scientific results than work done by a single investigator or an isolated team.My advice is intended for early-career scientists.The product of the collaboration may be high-impact research publications,enhanced geophysical monitoring capabilities in a foreign country,or an advanced training course.Choosing the right international partner is the most important step.Keeping an open mind and being receptive to suggestions to modify the initial concept is critical.Other key steps include having a mutually agreed upon plan with achievable goals and well-defined expected outcomes.International cooperation is a richly rewarding experience that accelerates progress in the Earth Sciences.
基金Supported by the Appropriate Technology Promotion Program in Chongqing,No.2023jstg005.
文摘BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram using internal and external validation to predict survival in patients with ampullary adenocarcinoma.METHODS Data were sourced from the surveillance,epidemiology,and end results stat database.The patients in the database were randomized in a 7:3 ratio into training and validation groups.Using Cox regression univariate and multivariate analyses in the training group,we identified independent risk factors for overall survival and cancer-specific survival to develop the nomogram.The nomogram was validated with a cohort of patients from the First Affiliated Hospital of the Army Medical University.RESULTS For overall and cancer-specific survival,12(sex,age,race,lymph node ratio,tumor size,chemotherapy,surgical modality,T stage,tumor differentiation,brain metastasis,lung metastasis,and extension)and 6(age;surveillance,epidemiology,and end results stage;lymph node ratio;chemotherapy;surgical modality;and tumor differentiation)independent risk factors,respectively,were incorporated into the nomogram.The area under the curve values at 1,3,and 5 years,respectively,were 0.807,0.842,and 0.826 for overall survival and 0.816,0.835,and 0.841 for cancer-specific survival.The internal and external validation cohorts indicated good consistency of the nomogram.CONCLUSION The dynamic nomogram offers robust predictive efficacy for the overall and cancer-specific survival of ampullary adenocarcinoma.
文摘Journal of Future Foods(ISSN 2772-5669.Owner:Bejjing Academy of Food Sciences.Production and Hosting:Elsevier B.V.on bchalf of KcAi Communications Co,Ltd.)is an intecrnational,pcer-reviewed open access journal bclonging to the disciplinc of food scicnce and technology.The aim of the journal is to report latcst rescarch results of high-tcch in food science.We welcome submissions that drive the ficld of food science towards whole food nutrition,intelligencc and high technology.
文摘Retrieval analysis in total knee arthroplasty(TKA)has been little studied in the literature.A narrative review of the literature to understand the current importance of retrieval analysis in TKA has been conducted.On August 27,2024,a literature search was performed in PubMed using“TKA retrieval analysis”as keywords.A total of 160 articles were found,of which only 19 were analyzed because they were directly related to the subject of this article.Rotating-platform(mobile-bearing)TKA has no surface damage advantage over fixed-bearing TKA.TKAs with central locking mechanisms are more prone to debond from the cement mantle.No major wear of the polyethylene(PE)component in TKA using oxidized zirconium components occurs.Femoral components of cobalt-chromium roughen more than oxidized zirconium femoral components.The use of a polished tibial tray over an unpolished design is advised.At short-run assessment(15 months on average),antioxidant-stabilized highly crosslinked PE components are not clinically different in surface damage,density of crosslinking,or oxidation compared to standard remelted highly crosslinked PE components.A correlation between implant position and PE component surface damage has been reported.It shows the importance of optimizing component position to reduce PE component damage.Contemporary knee tumor megaendoprostheses show notable volumetric metal wear originated at the rotating hinge.Retrieval analysis in TKA renders relevant data on how different prosthetic designs described in the literature perform.Such information can help to improve future prosthetic designs to increase prosthetic survival.
