Raman solitons in transient SRS

We report the observation of Raman solitons on numerical simulations of transient stimulated Raman scattering (TSRS) with small group velocity dispersion. The theory proceeds with the inverse scattering transform (IST) for initial-boundary value problems and it is shown that the explicit theoretical solution obtained by IST for a semi-infinite medium fits strikingly well the numerical solution for a finite medium. We understand this from the rapid decrease of the medium dynamical variable (the potential of the scattering theory). The spectral transform reflection coefficient can be computed directly from the values of the input and output fields and this allows to see the generation of the Raman solitons from the numerical solution. We confirm the presence of these nonlinear modes in the medium dynamical variable by the use of a discrete spectral analysis.Comment: LaTex file, to appear in Inverse Problem

Nitric oxide synthase acutely regulates progesterone production by in vitro cultured rabbit corpora lutea

We examined the presence and the regulation of nitric oxide (NO) synthase (NOS) using in vitro cultured corpora lutea (CL) obtained from rabbits at days 4 and 9 of pseudopregnancy. The role of NO and NOS on steroidogenesis was also investigated using the same CL preparations after short-term incubations (30 min and 2 h) with the NO donor, sodium nitroprusside (NP), the NOS inhibitor, Nomega-nitro-l-arginine methyl ester (l-NAME) and prostaglandin (PG) F-2alpha. The basal NOS activity was greater in CL at day 4 than at day 9, and was also differently modulated by PGF-2alpha, depending on the age of the CL. The addition of PGF-2alpha to day 4 CL had no effect, but PGF-2alpha on day 9 caused a threefold increase in NOS activity. NP caused a two- to fivefold decrease in release of progesterone from CL of both ages, and this inhibitory effect on steroidogenesis was reversed by l-NAME. All treatments failed to modify basal androgens and 17beta-oestradiol was not detectable in either control or treated CL. These results suggest that NO is effectively involved in the regulation process of steroidogenesis, independently of 17beta-oestradiol. PGF-2alpha had no effect on day 4, but induced luteolysis on day 9, by reducing progesterone (P</=0. 01) to about 18% of control. The luteolytic action of PGF-2alpha was completely reversed by co-incubation with l-NAME, thus supporting the hypothesis that luteolysis is mediated by NO. The addition of NP or l-NAME did not modify the in vitro release of PGF-2alpha. We hypothesised that PGF-2alpha upregulates NOS activity and, consequently, the production of NO, which acutely inhibits progesterone release from day 9 CL of pseudopregnant rabbits

A necessary condition for H∞H^\infty well-posedness of p-evolution equations

We consider p-evolution equations, for $p\geq2$, with complex valued coefficients. We prove that a necessary condition for $H^\infty$ well-posedness of the associated Cauchy problem is that the imaginary part of the coefficient of the subprincipal part (in the sense of Petrowski) satisfies a decay estimate as x goes to infinity

On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed

The different effects of linseed and fish oil supplemented diets on insulin sensitivity of rabbit does during pregnancy

This study investigates the effects of linseed (rich in ɑ-linolenic acid (ALA)) and fish oil (rich in eicosapentaenoic (EPA) and docosahexaenoic acid (DHA)) supplementation on the insulin resistance of pregnant rabbits. Two months before insemination, the rabbits (15 animals/group) were fed different diets: commercial standard (group C), supplemented with 10% extruded linseed (group L), and 3% fish oil (group FO). The L group does showed both the highest feed intake before AI (P &lt; 0.01) and the highest body weight (BW) throughout pregnancy (P &lt; 0.001). The L does yielded less milk than the C does (P &lt; 0.001); however, no differences were observed in either weight or size of litter at weaning. Regardless of diet, insulin concentrations and HOMA-IR values were higher during the first half of pregnancy (P &lt; 0.001). Nevertheless, the L does showed higher mean insulin concentrations than FO rabbits (P &lt; 0.01) and the lowest glucose clearance (P &lt; 0.01) during pregnancy. On the other hand, pregnant FO rabbits showed the lowest glucose concentrations (P &lt; 0.05) and the lowest Homeostasis model assessment values for insulin resistance (HOMA-IR, P &lt; 0.05) as well as a faster restoration of baseline glucose levels following glucose load (P &lt; 0.001). Before and during pregnancy, the BW of the rabbits was positively related to fasting sample- and tolerance test-derived indices of insulin resistance (P &lt; 0.05) suggesting that a high pre-pregnancy BW predisposes to gestational insulin resistance. Linseed supplementation increased BW and predisposed to insulin resistance during pregnancy; whereas, fish oil improved insulin sensitivity without significant changes in BW

Performance and behaviour of rabbit does in a group-housing system with natural mating or artificial insemination

This study compared reproductive performance and behaviour of does raised in a group-housing system and in a regular cage system. The group-housing pen was divided into different functional areas for suckling, resting, and eating and special hiding areas for kits when they had left the nest-boxes and does to favour the species specific behavioural traits. Does had access to their nest-box by means of an individual Electronic Nest-box Recognition System (ENRS) activated by a coded transponder placed in their eartags. Eight does were housed in each pen. Natural mating (NM, with a buck in the group) or artificial inseminations (AI) were applied. Litter size, kit mortality and kit weight at 14 d of age were similar for group-housing and cages when NM were applied. With a natural reproduction rhythm group-housing led to an increase of +38% of litters. However, from a management point of view, a cycled production system with AI is preferred. With AI and group-housing, a lower kindling rate and a lower kit weight at weaning were found. The lower kindling rate was partly caused by pseudo-pregnancies that were found in 23% (P &lt; 0.01) of the does in the group-housing system against 0% in the control group. Sixteen to 20% of the does in the group-housing system had skin injuries, which is an indicator for aggression among does. Most of the injuries were seen on the body and most of them were superficial bites. Based on the results of this study, it can be concluded that group-housing of rabbit does seems possible, but more research is needed to solve the problems of the decreased kindling rate and occurrence of pseudo-pregnancies, the lower weight at weaning and aggressiveness among does

Ablowitz-Ladik system with discrete potential. I. Extended resolvent

Ablowitz-Ladik linear system with range of potential equal to {0,1} is considered. The extended resolvent operator of this system is constructed and the singularities of this operator are analyzed in detail.Comment: To be published in Theor. Math. Phy

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

[EN] We use techniques from time-frequency analysis to show that the space S(omega )of rapidly decreasing omega-ultradifferentiable functions is nuclear for every weight function omega(t) = o(t) as t tends to infinity. Moreover, we prove that, for a sequence (M-p)(p) satisfying the classical condition (M1) of Komatsu, the space of Beurling type S-(M)p when defined with L-2 norms is nuclear exactly when condition (M2)' of Komatsu holds.We thank the reviewer very much for the careful reading of our manuscript and the comments to improve the paper. The first three authors were partially supported by the Project FFABR 2017 (MIUR), and by the Projects FIR 2018 and FAR 2018 (University of Ferrara). The first and third authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The research of the second author was partially supported by the project MTM2016-76647-P and the grant BEST/2019/172 from Generalitat Valenciana. The fourth author is supported by FWF-project J 3948-N35.Boiti, C.; Jornet Casanova, D.; Oliaro, A.; Schindl, G. (2021). Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis. Collectanea mathematica. 72(2):423-442. https://doi.org/10.1007/s13348-020-00296-0S423442722Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. London Math. Soc. 2(78), 392–406 (2008)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446, 920–944 (2017)Boiti, C., Jornet, D., Oliaro, A.: The Gabor wave front set in spaces of ultradifferentiable functions. Monatsh. Math. 188(2), 199–246 (2019)Boiti, C., Jornet, D., Oliaro, A.: About the nuclearity of $$\cal{S}_{(M_{p})}$$ and $$\cal{S}_{\omega }$$. In: Boggiatto, P., et al. (eds.) Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis, pp. 121–129. Birkhäuser, Cham (2020)Boiti, C., Jornet, D., Oliaro, A.: Real Paley-Wiener theorems in spaces of ultradifferentiable functions. J. Funct. Anal. 278(4), 108348 (2020)Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Result. Math. 17, 206–237 (1990)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Math. 167(2), 99–131 (2005)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)Franken, U.: Weight functions for classes of ultradifferentiable functions. Results Math. 25, 50–53 (1994)Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)Gröchenig, K., Leinert, M.: Wiener’s Lemma for twisted convolution and Gabor frames. J. Am. Math. Soc. 17(1), 1–18 (2004)Gröchenig, K., Zimmermann, G.: Spaces of Test Functions via the STFT. J. Funct. Spaces Appl. 2(1), 25–53 (2004)Heinrich, T., Meise, R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364–387 (2007)Hörmander, L.: Notions of Convexity. Progress in Mathematics, vol. 127. Birkhäuser, Boston (1994)Janssen, A.J.E.M.: Duality and Biorthogonality for Weyl-Heisenberg Frames. J. Fourier Anal. Appl. 1(4), 403–436 (1995)Komatsu, H.: Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect IA Math. 20, 25–105 (1973)Langenbruch, M.: Hermite functions and weighted spaces of generalized functions. Manuscripta Math. 119(3), 269–285 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Petzsche, H.J.: Die nuklearität der ultradistributionsräume und der satz vom kern I. Manuscripta Math. 24, 133–171 (1978)Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)Pilipović, S., Prangoski, B., Vindas, J.: On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution. J. Math. Pures Appl. 116, 174–210 (2018)Rodino, L.: Linear Partial Differential Operators in Gevrey Spaces. World Scientific Publishing Co. Inc, River Edge, NJ (1993)Rodino, L., Wahlberg, P.: The Gabor wave front set. Monatsh. Math. 173, 625–655 (2014)Schmets, J., Valdivia, M.: Analytic extension of ultradifferentiable Whitney jets. Collect. Math. 50(1), 73–94 (1999

The Gabor wave front set in spaces of ultradifferentiable functions

[EN] We consider the spaces of ultradifferentiable functions S as introduced by Bjorck (and its dual S) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: global regularity properties of pseudodifferential operators of infinite order and the micro-pseudolocal behaviour of partial differential operators with polynomial coefficients and of localization operators with symbols of exponential growth. Moreover, we prove that the new wave front set, defined in terms of the Gabor transform, can be described using only Gabor frames. Finally, some examples show the convenience of the use of weight functions to describe more precisely the global regularity of (ultra)distributions.The authors were partially supported by the INdAM-Gnampa Project 2016 "Nuove prospettive nell'analisi microlocale e tempo-frequenza", by FAR2013, FAR2014 (University of Ferrara) and by the project "Ricerca Locale - Analisi di Gabor, operatori pseudodifferenziali ed equazioni differenziali" (University of Torino). The research of the second author was partially supported by the project MTM2016-76647-P.Boiti, C.; Jornet Casanova, D.; Oliaro, A. (2019). The Gabor wave front set in spaces of ultradifferentiable functions. Monatshefte für Mathematik. 188(2):199-246. https://doi.org/10.1007/s00605-018-1242-3S1992461882Albanese, A., Jornet, D., Oliaro, A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. Theory 66, 153–181 (2010)Albanese, A., Jornet, D., Oliaro, A.: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Math. Nachr. 285(4), 411–425 (2012)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)Boiti, C., Gallucci, E.: The overdetermined Cauchy problem for $$\omega$$ ω -ultradifferentiable functions. Manuscripta Math. 155(3-4), 419–448 (2018)Boiti, C., Jornet, D.: A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions. J. Pseudo-Differ. Oper. Appl. 8(2), 297–317 (2017)Boiti, C., Jornet, D.: A characterization of the wave front set defined by the iterates of an operator with constant coefficients. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 111(3), 891–919 (2017)Boiti, C., Jornet, D., Juan-Huguet, J.: Wave front sets with respect to the iterates of an operator with constant coefficients. Abstr. Appl. Anal. 2014, 1–17 (2014). https://doi.org/10.1155/2014/438716Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446, 920–944 (2017)Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization. Theory and Examples, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, New York (2006)Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Result. Math. 17, 206–237 (1990)Cappiello, M., Schulz, R.: Microlocal analysis of quasianalytic Gelfand–Shilov type ultradistributions. 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Ovulation induction in rabbit does: current knowledge and perspectives

The profitability of rabbit farms has increased in recent years due primarily to improvements in the management of reproduction and genetic selection. This review summarizes the most important scientific papers relating to ovulation in rabbit does dealing in particular with: (a) studies from 1905 to the present day relating to ovulatory mechanisms in rabbit does; (b) research on the primary gonadotrophin-releasing hormone (GnRH), its analogues and their functions; and (c) descriptions of parenteral and intravaginal (iv.) treatments for induction of ovulation in does and their reported efficacies. The addition of GnRH analogues via the seminal dose (iv.) fulfils the need for a welfare-orientated method of inducing ovulation in rabbits. The structure, tissues, secretions, contractions, and innervations of the vagina in rabbits that can affect absorption profiles are reviewed in the context of recent reports of the achievement of high ovulation rates obtained by adding GnRH analogues directly to the seminal dose. This review demonstrates the possibility of ovulation induction in rabbits by the addition of GnRH synthetic analogues to the seminal doses and provides new perspectives for simplifying the AI technique