Representations of an integer by some quaternary and octonary quadratic forms

In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.Comment: 20 pages, 4 tables. arXiv admin note: text overlap with arXiv:1607.0380

Cauchyness and convergence in fuzzy metric spaces

[EN] In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.Almanzor Sapena acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant TEC2013-45492-R. Valentín Gregori acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant MTM 2012-37894-C02-01.Gregori Gregori, V.; Miñana, J.; Morillas, S.; Sapena Piera, A. (2017). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(1):25-37. https://doi.org/10.1007/s13398-015-0272-0S25371111Alaca, C., Turkoglu, D., Yildiz, C.: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 29, 1073–1078 (2006)Edalat, A., Heckmann, R.: A computational model for metric spaces. Theor. Comput. Sci. 193, 53–73 (1998)Engelking, R.: General topology. PWN-Polish Sci. Publ, Warsawa (1977)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)George, A., Veeramani, P.: Some theorems in fuzzy metric spaces. J. Fuzzy Math. 3, 933–940 (1995)George, A., Veeramani, P.: On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365–368 (1997)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485–489 (2000)Gregori, V., Romaguera, S.: On completion of fuzzy metric spaces. Fuzzy Sets Syst. 130, 399–404 (2002)Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces. Fuzzy Sets Syst. 144, 411–420 (2004)Gregori, V., López-Crevillén, A., Morillas, S., Sapena, A.: On convergence in fuzzy metric spaces. Topol. Appl. 156, 3002–3006 (2009)Gregori, V., Miñana, J.J.: Some concepts realted to continuity in fuzzy metric spaces. In: Proceedings of the conference in applied topology WiAT’13, pp. 85–91 (2013)Gregori, V., Miñana, J.-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces (2015, submitted)Gregori, V., Miñana, J.-J.: std-Convergence in fuzzy metric spaces. Fuzzy Sets Syst. 267, 140–143 (2015)Gregori, V., Miñana, J.-J.: Strong convergence in fuzzy metric spaces Filomat (2015, accepted)Gregori, V., Miñana, J.-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets Syst. 204, 71–85 (2012)Gregori, V., Miñana, J.-J., Morillas, S.: A note on convergence in fuzzy metric spaces. Iran. J. Fuzzy Syst. 11(4), 75–85 (2014)Gregori, V., Morillas, S., Sapena, A.: On a class of completable fuzzy metric spaces. Fuzzy Sets Syst. 161, 2193–2205 (2010)Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metric spaces and applications. Fuzzy Sets Syst. 170, 95–111 (2011)Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326–334 (1975)Mihet, D.: On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915–921 (2007)Mihet, D.: Fuzzy $$\varphi$$ φ -contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 159, 739–744 (2008)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431–439 (2004)Mishra, S.N., Sharma, N., Singh, S.L.: Common fixed points of maps on fuzzy metric spaces Internat. J. Math. Math. Sci. 17(2), 253–258 (1994)Morillas, S., Sapena, A.: On Cauchy sequences in fuzzy metric spaces. In: Proceedings of the conference in applied topology (WiAT’13), pp. 101–108 (2013)Ricarte, L.A., Romaguera, S.: A domain-theoretic approach to fuzzy metric spaces. Topol. Appl. 163, 149–159 (2014)Sherwood, H.: On the completion of probabilistic metric spaces. Z.Wahrschein-lichkeitstheorie verw. Geb. 6, 62–64 (1966)Sherwood, H.: Complete Probabilistic Metric Spaces. Z. Wahrschein-lichkeitstheorie verw. Geb. 20, 117–128 (1971)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003)Veeramani, P.: Best approximation in fuzzy metric spaces. J. Fuzzy Math. 9, 75–80 (2001

Neurogenic bladder in patients with traumatic spinal cord injury: Treatment and follow-up

Study design:Multi-center, cross-sectional study.Objectives:Our aim was to evaluate the treatment methods and follow-up of neurogenic bladder in patients with traumatic spinal cord injury retrospectively using a questionnaire.Setting: Turkey.Methods:Three hundred and thirty-seven patients who had spinal cord injury for at least 2 years were enrolled from six centers in the neurogenic bladder study group. They were asked to fill-out a questionnaire about treatments they received and techniques they used for bladder management.Results:The study included 246 male and 91 female patients with a mean age of 42±14 years. Intermittent catheterization ( IC) was performed in 77.9% of the patients, 3.8% had indwelling catheters, 13.8% had normal spontaneous micturition, 2.6% performed voiding maneuvers, 1.3% used diapers and 0.6% used condom catheters. No gender difference was found regarding the techniques used in bladder rehabilitation ( P>0.05). Overall, 63.2% of patients used anticholinergic drugs; anticholinergic drug use was similar between genders ( P>0.05). The most common anticholinergic drug used was oxybutynin ( 40.3%), followed by trospium ( 32.6%), tolterodine ( 19.3%) darifenacin ( 3.3%), propiverine ( 3.3%) and solifenacin ( 1.1%). The specialties of the physicians who first prescribed the anticholinergic drug were physiatrists ( 76.2%), urologists ( 22.1%) and neurologists ( 1.7%). Only four patients had previously received injections of botulinum-toxin-A into the detrusor muscle and three of them stated that their symptoms showed improvement. Most of the patients ( 77%) had regular follow-up examinations, including urine cultures, urinary system ultrasound and urodynamic tests, when necessary; the reasons for not having regular control visits were living distant from hospital ( 15.3%) and monetary problems ( 7.7%). Of the patients, 42.7% did not experience urinary tract infections ( UTI), 36.4% had bacteriuria but no UTI episodes with fever, 15.9% had 1-2 clinical UTI episodes per year and 5% had ≥3 clinical UTIs. The clinical characteristics of patients with and without UTI ( at least one symptomatic UTI during 1 year) were similar ( P>0.05). The frequency of symptomatic UTI was similar in patients using different bladder management techniques ( P>0.05).Conclusion:The most frequently used technique for bladder rehabilitation in patients with SCI was IC ( 77.9%). In all, 63.2% of patients used anticholinergic drugs, oxybutynin being the most commonly used drug. Also, 77% of patients had regular control visits for neurogenic bladder; 42.7% did not experience any UTIs. © 2014 International Spinal Cord Society

Intermittent catheterization in patients with traumatic spinal cord injury: Obstacles, worries, level of satisfaction

Objectives: The aim of this study is to examine the obstacles in people with traumatic spinal cord injury (SCI) face performing intermittent catheterization (IC), also their worries and level of satisfaction. Methods: Two hundred sixty-nine patients performing IC for at least 3 months were asked to fill-out a questionnaire about their opinions on IC. Results: In total, 69.5% of patients performed IC themselves, 10.4% had performed by their mothers, 7.8% by another caregiver and 7.4% by their spouse. For the 72 (26%) patients unable to apply IC, reasons were insufficient hand function (56.1%), being unable to sit appropriately (35.4%) and spasticity (8.5%). In all, 70% of male patients had insufficient hand function, 20% could not sit and 10% had spasticity while 56.3% of female patients could not sit, 37.5% had insufficient hand function and 63% had spasticity. Difference between sexes was found to be statistically significant (P<0.05). Worries patients had when starting IC were fear of being dependent on IC (50.2%), accidentally injuring self (43.8%), embarrassment (43.2%), causing an infection (40.2%), bleeding (32.7%), fear of feeling pain (30.2%) and hygiene (24.7%). More women felt embarrassment; other items were similar in both sexes. In all, 46.9% of patients had urinary incontinence in intervals. Conclusion: In total, 69.5% of patients performed IC themselves. Men's most common obstacle was insufficient hand function while women's was being unable to sit appropriately. Patients' most common worries were being dependent on IC for life. In all, 46.9% had incontinence in intervals; 47.9% said IC improved their life quality; and 97.4% preferred IC over continuous catheterization. © 2014 International Spinal Cord Society All rights reserved