Metabolic effects of dialyzate glucose in chronic hemodialysis: results from a prospective, randomized crossover trial

Background. There is no agreement concerning dialyzate glucose concentration in hemodialysis (HD) and 100 and 200 mg/dL (G100 and G200) are frequently used. G200 may result in diffusive glucose flux into the patient, with consequent hyperglycemia and hyperinsulinism, and electrolyte alterations, in particular potassium (K) and phosphorus (P). This trial compared metabolic effects of G100 versus G200. Methods. Chronic HD patients participated in this randomized, single masked, controlled crossover trial (www.clinicaltrials.gov: #NCT00618033) consisting of two consecutive 3-week segments with G100 and G200, respectively. Intradialytic serum glucose (SG) and insulin concentrations (SI) were measured at 0, 30, 60, 120, 180, 240 min and immediately post-HD; P and K were measured at 0, 120, 180 min and post-HD. Hypoglycemia was defined as an SG <70 mg/dL. Mean SG and SI were computed as area under the curve divided by treatment time. Results. Fourteen diabetic and 15 non-diabetic subjects were studied. SG was significantly higher with G200 as compared to G100, both in diabetic {G200: 192.8 ± 48.1 mg/dL; G100: 154.0 ± 27.3 mg/dL; difference 38.8 [95% confidence interval (CI): 21.2-56.4] mg/dL; P < 0.001} and non-diabetic subjects [G200: 127.0 ± 11.2 mg/dL; G100 106.5 ± 10.8 mg/dL; difference 20.6 (95% CI: 15.3-25.9) mg/dL; P < 0.001]. SI was significantly higher with G200 in non-diabetic subjects. Frequency of hypoglycemia, P and K serum levels, interdialytic weight gain and adverse intradialytic events did not differ significantly between G100 and G200. Conclusion. G200 may exert unfavorable metabolic effects in chronic HD patients, in particular hyperglycemia and hyperinsulinism, the latter in non-diabetic subject

Nonlinear Fredholm equations in modular function spaces

We investigate the existence of solutions in modular function spaces of the Fredholm integral equation $$\Phi(\theta) = g(\theta) + \int^1_0 f(\theta,\sigma, \Phi(\sigma)) \,d\sigma,$$ where $\Phi(\theta), g(\theta)\in L_{\rho}, \theta\in [0,1], f: [0,1]\times[0,1]\times L_{\rho}\to \mathbb{R}$. An application in the variable exponent Lebesgue spaces is derived under minimal assumptions on the problem data

On Periodic Solutions of Delay Differential Equations with Impulses

The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces R ( [ &#8722; r , 0 ] , R n ) . The existence of the periodic solution of impulsive delay differential equations is obtained by using the Sch&#228;ffer fixed point theorem in regulated space R ( [ &#8722; r , 0 ] , R n ) . </inline-formula

V-Proximal Trustworthy Banach Spaces

In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all Lp spaces 1<p<∞ as well as the sequence spaces lp1<p<∞, the Sobolev spaces Wp,n1<p<∞, and the Schatten trace ideals Cp1<p<∞

Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385&ndash;398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269&ndash;1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699&ndash;29]

V-Prox-Regular Functions in Smooth Banach Spaces

In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V-prox-regularity of a given l.s.c. f and the V-prox-regularity of its epigraph

Modular Uniform Convexity in Every Direction in Lp(·) and Its Applications

We prove that the Lebesgue space of variable exponent L p ( &middot; ) ( &Omega; ) is modularly uniformly convex in every direction provided the exponent p is finite a.e. and different from 1 a.e. The notion of uniform convexity in every direction was first introduced by Garkavi for the case of a norm. The contribution made in this work lies in the discovery of a modular, uniform-convexity-like structure of L p ( &middot; ) ( &Omega; ) , which holds even when the behavior of the exponent p ( &middot; ) precludes uniform convexity of the Luxembourg norm. Specifically, we show that the modular &rho; ( u ) = &int; &Omega; | u ( x ) | d x possesses a uniform-convexity-like structure even if the variable exponent is not bounded away from 1 or &infin;. Our result is new and we present an application to fixed point theory

Delay differential equation in metric spaces: A partial ordered sets approach

In this paper we develop a fixed point theorem in the partially ordered vector metric space C([–τ , 0],Rn) by using vectorial norm. Then we use it to prove the existence of periodic solutions to nonlinear delay differential equations