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We consider a ratinonal map $\phi$ from m-dimensional projective space to n-dimensional projective space that is a parameterization of m-dimensional variety. Our main goal is to study the (m-1)-dimensional fibers of $\phi$ in relation with the m-th local cohomology modules of Rees algebra of its base ideal.

Abstract Using some recent results of fixed point of weakly contractive mappings on the partially ordered space, the existence and uniqueness of solution for interval fractional delay differential equations (IFDDEs) in the setting of the Caputo generalized Hukuhara fractional differentiability are studied. The dependence of the solution on the order and the initial condition of IFDDE is shown. A new technique is proposed to find the exact solutions of IFDDE by using the solutions of interval integer order delay differential equation. Finally, some examples are given to illustrate the applications of our results.

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.

We consider the random fuzzy differential equations (RFDEs) with impulses. Using Picard method of successive approximations, we shall prove the existence and uniqueness of solutions to RFDEs with impulses under suitable conditions. Some of the properties of solution of RFDEs with impulses are studied. Finally, an example is presented to illustrate the results.

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

STUDY QUESTION Among couples with infertility and normal total sperm count and motility, can sperm morphology be used as a biomarker to identify couples who benefit more from ICSI over conventional IVF (c-IVF) on fertility outcomes? SUMMARY ANSWER Based on this secondary analysis of a large randomized clinical trial (RCT), sperm morphology has limited value as a biomarker to identify couples who benefit more from ICSI over c-IVF on live birth, ongoing pregnancy, clinical pregnancy or total fertilization failure. WHAT IS KNOWN ALREADY Our recent RCT showed that ICSI did not result in higher live birth rates in couples with normal total sperm count and motility. It is unclear whether sperm morphology can be used as a biomarker to identify couples who benefit more from ICSI over c-IVF in this population. STUDY DESIGN, SIZE, DURATION This was a secondary analysis of an open-label, multi-centre, RCT comparing ICSI versus c-IVF in 1064 couples with infertility and normal total sperm count and motility. In this secondary study, we evaluated the effectiveness of ICSI over c-IVF in relation to sperm morphology. PARTICIPANTS/MATERIALS, SETTING, METHODS Couples were eligible if they had ≤2 previous IVF/ICSI attempts, and the male partner had normal total sperm count and motility according to the fifth edition of the WHO laboratory manual for the examination and processing of human semen. Sperm morphology was measured from samples obtained during the first consultation and data for sperm morphology were available in partners of all participants in this trial. The outcomes of interest were live birth, ongoing pregnancy, clinical pregnancy, and total fertilization failure. We first conducted a logistic regression analysis with an interaction term (sperm morphology as a continuous variable by treatment (ICSI versus c-IVF)) on the four outcomes. We also used restricted cubic spline analysis to evaluate non-linear interaction and plotted the treatment effects of ICSI over c-IVF at different sperm morphology levels and the predicted probability of these outcomes in both ICSI and c-IVF groups. MAIN RESULTS AND THE ROLE OF CHANCE The median proportion of sperm with normal morphology in both groups was 3% (Interquartile range 1–6%). Live birth rates were (184/532) 34.6% for ICSI versus (166/532) 31.2% for c-IVF. No significant interaction was found between sperm morphology and treatment effect of ICSI versus c-IVF on the rates of live birth, ongoing pregnancy, clinical pregnancy, and total fertilization failure (P  = 0.181, 0.153, 0.168, and 0.788 respectively). In the analyses using restricted cubic splines, no evidence of interaction between sperm morphology and the treatment effect was found. Interaction figures showed that the treatment effect of ICSI over c-IVF at different sperm morphology levels was fluctuating around no effect line, and the predicted outcomes for the two groups were mostly overlapping at different sperm morphology levels. LIMITATIONS AND REASONS FOR CAUTION This secondary analysis may be underpowered to detect a difference in treatment effects at different sperm morphology levels due to relatively small number of events at some sperm morphology levels. Moreover, sperm morphology assessment was performed during the first consultation, rather than on the day of randomization. WIDER IMPLICATIONS OF THE FINDINGS In couples with infertility and normal total sperm count and motility, sperm morphology has a limited role as a biomarker to identify couples who benefit more from ICSI over c-IVF on fertility outcomes. STUDY FUNDING/COMPETING INTEREST(S) This study was funded by My Duc Hospital, Ho Chi Minh City, Vietnam. RW was supported by an NHMRC EL Investigator Grant (GNT2009767). LNV has received speaker and conference fees from Merck, grant, speaker, conference fees from Merck Sharpe and Dohme, and speaker, conference, and scientific board fees from Ferring. TMH has received speaker fees from Merck, Merck Sharp Dohme, and Ferring. BWM reports consultancy, travel support and research funding from Merck and consultancy for Organon and Norgine. BWM holds stock from ObsEva. TRIAL REGISTRATION NUMBER NCT03428919 [ABSTRACT FROM AUTHOR]

This study demonstrates the existence and uniqueness of solutions to stochastic fuzzy fractional integral equations and investigates some of their properties. [ABSTRACT FROM AUTHOR]

We present a heuristic approach to formulate physical fields from systems of first order linear partial differential equations by considering the symmetric and antisymmetric properties of the matrices that represent the systems of equations. Particularly, we show that Maxwell and Dirac fields can be established by imposing different types of symmetric and antisymmetric conditions on their associated representing matrices. [ABSTRACT FROM AUTHOR]

Microclimate has a substantial impact on plant composition, survival, and growth, as well as ecosystem processes. Although microclimatic conditions in anthropogenically fragmented ecosystems have received considerable scientific attention, they are understudied in naturally fragmented ecosystems, including forest-steppes. In addition, earlier investigations in these mosaics only measured microclimate parameters for a very short period (i.e., 24 hours on a single summer day). In the present study, the long-term microclimatic conditions were described in multiple habitat types, both woody and non-woody, in a sandy forest-steppe ecosystem in the Kiskunság, central Hungary. The aim of this study was to answer (1) how air humidity and temperature conditions differ among the studied habitats during the growing season and (2) which habitats are more stressed to vegetation growth regarding vapor pressure deficit (VPD). Wireless sensors recording air temperature and humidity values were used to monitor microclimatic parameters. VPD values were calculated based on the obtained air temperature and humidity, and two thresholds at 1.2 and 3.0 kPa were defined. To compare mean air temperature and humidity variables, as well as above-threshold VPD rate among habitat types, general linear models were used. Our results indicated that open grasslands were the warmest and driest habitats. Among woody habitats, south-facing edges had the harshest microclimatic conditions. The current work also found that small forest patches and larger Microclimate has a substantial impact on plant composition, survival, and growth, as well as ecosystem processes. Although microclimatic conditions in anthropogenically fragmented ecosystems have received considerable scientific attention, they are understudied in naturally fragmented ecosystems, including forest-steppes. In addition, earlier investigations in these mosaics only measured microclimate parameters for a very short period (i.e., 24 hours on a single summer day). In the present study, the long-term microclimatic conditions were described in multiple habitat types, both woody and non-woody, in a sandy forest-steppe ecosystem in the Kiskunság, central Hungary. The aim of this study was to answer (1) how air humidity and temperature conditions differ among the studied habitats during the growing season and (2) which habitats are more stressed to vegetation growth regarding vapor pressure deficit (VPD). Wireless sensors recording air temperature and humidity values were used to monitor microclimatic parameters. VPD values were calculated based on the obtained air temperature and humidity, and two thresholds at 1.2 and 3.0 kPa were defined. To compare mean air temperature and humidity variables, as well as above-threshold VPD rate among habitat types, general linear models were used. Our results indicated that open grasslands were the warmest and driest habitats. Among woody habitats, south-facing edges had the harshest microclimatic conditions. The current work also found that small forest patches and larger. [ABSTRACT FROM AUTHOR]

We present a general formulation of special relativity with generalized Lorentz transformations and Minkowski line element. Besides the Minkowski and Euclidean metrics associated, respectively, with the Lorentz and Euclidean transformations, the general formulation can also be used to establish new forms of coordinate transformations that also leave their associated metrics invariant. We also formulate relativistic mechanics under the framework of the generalized special relativity. [ABSTRACT FROM AUTHOR]

This paper reports the results of a quasi-experimental effects-of-instruction study examining the efficacy of applying a Cognitive Linguistic (CL) approach to L2 learning of the semantics of English modals. In spite of their frequency in typical input, modal verbs present L2 learners with difficulties, party due to their inherent complexity--modals typically have two divergent senses--a root sense and an epistemic sense. ELT textbooks and most grammar books aimed at L2 teachers present the two meanings as homophones, failing to address any systematic semantic patterning in the modal system as a whole. Additionally, ELT texts tend to present modals from a speech act perspective. In contrast, CL analyses (e.g., Langacker 1991; Nuyts 2001; Sweetser 1990; Talmy 1988) offer both a systematic, motivated representation of the relationship between the root and epistemic meanings and a rather precise representation of the semantics of each modal. To test the pedagogical effectiveness of a CL account of modals, an effects-of-instruction study was conducted with three groups of adult, high-intermediate ESL learners: a Cognitive treatment group, a Speech Acts treatment group, and a Control group. Results of an ANCOVA indicated that the Cognitive treatment group demonstrated significantly more improvement than the Speech Acts treatment group. The experiment thus lends empirical support for the position that CL, in addition to offering a compelling analytical account of language, may also provide the basis for more effective grammar instruction than that found in most current ELT teaching materials. (Contains 3 tables, 5 figures, and 7 notes.)

In this paper, we aim to prove the existence, uniqueness of the solution to the random delay differential equation of fractional order involving the successive approximation method. Moreover, using the Gronwall inequality, we study the continuous dependence of solution in the mean square sense of the problem. Finally, the fractional ϵ-approximate solution in the mean square sense is also considered. [ABSTRACT FROM AUTHOR]