The multivariate moment problem is investigated in the general context of the polynomial algebra ... more The multivariate moment problem is investigated in the general context of the polynomial algebra R[x i | i ∈ Ω] in an arbitrary number of variables x i , i ∈ Ω. The results obtained are sharpest when the index set Ω is countable. Extensions of Haviland's theorem [13] and Nussbaum's theorem [28] are proved. Lasserre's description of the support of the measure in terms of the non-negativity of the linear functional on a quadratic module of R[x i | i ∈ Ω] in [21] is shown to remain valid in this more general situation. The main tool used in the paper is an extension of the localization method developed by the third author in [24], [26] and [27]. Various results proved in [24], [26] and [27]
POSTERS or hydrophobic bile salts (GCDC). IGF1 isoforms were analyzed by realtime PCR by using b-... more POSTERS or hydrophobic bile salts (GCDC). IGF1 isoforms were analyzed by realtime PCR by using b-actin as internal reference. At least 3 different IGF1 isoforms were identified. In both hepatocytes and cholangiocytes, the "locally acting" IGF1 isoform (XO6108) and circulating IGF1 isoform (NM_178866) represented respectively 44% and 52% of the total IGF1. Basal mRNAs for both "locally acting" and circulating IGF1 isoform were 10-fold higher in hepatocytes than cholangiocytes. After BDL for 3 hrs, the "locally acting" IGF1 isoform decreased 3-fold in hepatocytes but remains stable in cholangiocytes (p < 0.05). After 1 week BDL, hepatocytes, which do not proliferate and show apoptotic damage, displayed a further 5-fold decrease of "locally acting" IGF1 mRNA. In contrast, cholangiocytes which markedly proliferate showed a 8-fold increase of the "locally acting" IGF1 mRNA. The effect of 3 hours BDL on IGF1 isoforms was reproduced in vitro by incubation with glycochenodeoxycholate (GCDC). The cytotoxic effects (inhibition of proliferation and induction of apoptosis) of GCDC on isolated cholangiocytes were enhanced by selective silencing (SiRNA) of "locally acting", IGF1 isoform into higher extent than silencing of circulating IGF1 isoform. Conclusions: rat hepatocytes and cholangiocytes express the "locally acting" IGF1 isoform which decreased during cell damage and increased during cell proliferation. The "locally acting" IGF1 was more active than the circulating isoform in protecting cholangiocytes from GCDC-induced apoptosis. These findings indicates that, other than in muscle and neural tissues, also in liver cells the "locally acting" IGF1 isoform may play a major role in modulating response to damage.
In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide... more In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide (NO) system on the antidepressant-like effects of paroxetine in the mouse forced swimming test. Swim sessions were conducted by placing mice in individual glass cylinders filled with water for 6 min. The duration of behavioral immobility during the last 4 min of the test was evaluated. Paroxetine (8 and 16 mg/kg, intraperitoneal [i.p.]) significantly reduced the immobility times of mice, whereas lower doses (2 and 4 mg/kg) had no effect. NMDA antagonists MK-801 (0.1 and 0.25 mg/kg, i.p.) and ifenprodil (1 and 3 mg/kg, i.p.) and the NO synthase inhibitor NG-L-arginine methyl ester (L-NAME; 30 and 100 mg/kg, i.p.) significantly decreased the immobility time. Lower doses of MK-801 (0.01 and 0.05 mg/kg), ifenprodil (0.1 and 0.5 mg/kg), and L-NAME (10 mg/kg) had no effect. Combined treatment of subeffective doses of paroxetine (4 mg/kg) and MK-801 (0.05 mg/kg), ifenprodil (0.5 mg/kg), and L-NAME (10 mg/kg) robustly exerted an antidepressant-like effect. The noneffective dose of a NO precursor L: -arginine (750 mg/kg, i.p.) prevented the antidepressant-like effect of paroxetine (30 mg/kg). We suggested, for the first time, a possible role for NMDAR/NO signaling in the antidepressant-like effects of paroxetine, providing a new approach for the treatment of depression.
Let V be the countable dimensional polynomial R-algebra R[X] := R[X1, . . . , Xn]. Let τ be a loc... more Let V be the countable dimensional polynomial R-algebra R[X] := R[X1, . . . , Xn]. Let τ be a locally convex topology on V. Let K be a closed subset of R n , and let M := M {g 1 ,···gs} be a finitely generated quadratic module in V . We investigate the following question: When is the cone Psd(K) (of polynomials nonnegative on K) included in the closure of M ? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of M = R[X] 2 with respect to weighted norm-p topologies. We show that this closure coincides with the cone Psd(K) where K is a certain convex compact polyhedron. We use these results to generalize Berg's et al work on exponentially bounded moment sequences.
In [3] Berg, Christensen and Ressel prove that the closure of the cone of sums of squares R[X] 2 ... more In [3] Berg, Christensen and Ressel prove that the closure of the cone of sums of squares R[X] 2 in the polynomial ring R[X] := R[X 1 , . . . , Xn] in the topology induced by the 1 -norm is equal to Pos([−1, 1] n ), the cone consisting of all polynomials which are non-negative on the hypercube [−1, 1] n .
The purpose of this study was to investigate the effect of the endogenous cannabinoid anandamide ... more The purpose of this study was to investigate the effect of the endogenous cannabinoid anandamide on the nonadrenergic noncholinergic (NANC) relaxant responses to electrical field stimulation in isolated rat corpus cavernosum. The corporal strips were mounted under tension in a standard oxygenated organ bath with guanethidine sulfate (5 μM) and atropine (1 μM) (to produce adrenergic and cholinergic blockade). The strips were precontracted with phenylephrine hydrochloride (7.5 μM) and electrical field stimulation was applied at different frequencies to obtain NANC-mediated relaxation. The expression of CB 1 , CB 2 and vanilloid receptor proteins within the rat corpus cavernosum was evaluated using western blot analysis. The results showed that the relaxant responses to electrical stimulation were significantly enhanced in the presence of anandamide at 1 and 3 μM. The potentiating effect of anandamide (1 μM) on relaxation responses was significantly attenuated by either the selective cannabinoid CB 1 receptor antagonist N-(piperidin-1-yl)-5-(4-iodophenyl)-1-(2, 4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide (AM251; 1 μM) or the vanilloid receptor antagonist capsazepine (3 μM), but not by the selective cannabinoid CB 2 receptor antagonist 6-iodo-2methyl-1-[2-(4-morpholinyl) ethyl]-1H-indol-3-yl (4-methoxyphenyl)methanone (AM630; 1 μM). Neither of these antagonists had influence on relaxation responses. Indomethacin (20 μM) had no effect on NANC-mediated relaxation in the presence or absence of anandamide (1 μM). Preincubation with N w -Nitro-L-Arginine Methyl Ester (L-NAME; 1 μM) significantly inhibited the relaxation responses in the presence or absence of 1 μM anandamide. Although at 30 nM, L-NAME did not cause a significant inhibition of relaxant responses individually, it significantly inhibited the potentiating effect of anandamide (1 μM) on relaxation responses. Anandamide (1 μM) had no influence on concentration-dependent relaxant responses to sodium nitroprusside (10 nM-1 mM), a nitric oxide (NO) donor. The western blotting of corporal tissues demonstrated the existence of both vanilloid and CB 1 receptors in corporal strips. In conclusion, our results showed that anandamide has a potentiating effect on NANC-mediated relaxation of rat corpus cavernosum through both CB 1 and vanilloid receptors and the NO-mediated component of the NANC relaxant responses to electrical stimulation is involved in this enhancement.
We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo a... more We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points.
Background/Aims: The clinical relevance of QT prolongation, the most widely recognized cardiac el... more Background/Aims: The clinical relevance of QT prolongation, the most widely recognized cardiac electrophysiological abnormality of cirrhosis, is still undefined. The aim of this study is to examine the susceptibility of chronic (4-week) bile duct-ligated rats to epinephrine-induced arrhythmias. The roles of nitric oxide and endogenous opioids were also evaluated.
Berg, Christensen and Ressel prove that the closure of the cone of sums of squares in the ring of... more Berg, Christensen and Ressel prove that the closure of the cone of sums of squares in the ring of real polynomials in the topology induced by the $\ell_1$-norm is equal to the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$. The result is deduced as a corollary of a general result which is valid for any commutative semigroup. In later work Berg and Maserick and also Berg, Christensen and Ressel establish an even more general result, for a commutative semigroup with involution, for the closure of the cone of sums of squares of symmetric elements in the weighted $\ell_1$-seminorm topology associated to an absolute value. In the present paper we give a new proof of these results which is based on Jacobi's representation theorem. At the same time, we use Jacobi's representation theorem to extend these results from sums of squares to sums of 2d-powers, proving, in particular, that for any integer $d>0$, the closure of the cone of sums of 2d-powers in the ring of real polynomials in the topology induced by the $\ell_1$-norm is equal the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$.
Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which sa... more Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which satisfies $\rho(ab)\leq\rho(a)\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$ in the topology induced by $\rho$, for any integer $d\ge1$. We show that this closure is exactly the set of all elements $a\in A$ such that $\alpha(a)\ge0$ for every $\rho$-continuous $\mathbb{R}$-algebra homomorphism $\alpha : A \rightarrow \mathbb{R}$ with $\alpha(S)\subseteq[0,\infty)$, and that this result continues to hold when $\rho$ is replaced by any locally multiplicatively convex topology $\tau$ on $A$. We obtain a representation of any linear functional $L : A \rightarrow \reals$ which is continuous with respect to any such $\rho$ or $\tau$ and non-negative on $S$ as integration with respect to a unique Radon measure on the space of all real valued $\reals$-algebra homomorphisms on $A$, and we characterize the support of the measure obtained in this way.
Let $f,g_1,\dots,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,\dots,x_n]$. The paper d... more Let $f,g_1,\dots,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,\dots,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,\dots,m$. The paper shows that there is an algorithm for computing such a lower bound, based on geometric programming, which applies in a large number of cases. For example, the algorithm computes a lower bound for $f$ on a hypercube $\prod_{i=1}^n [-N_i,N_i]$, or, more generally, on any product of hyperellipsoids of a suitable form. The algorithm extends and generalizes earlier algorithms of Ghasemi and Marshall, dealing with the case $m=0$, and of Ghasemi, Lasserre and Marshall, dealing with the case $m=1$ and $g_1= M-(x_1^d+\dots+x_n^d)$. Here, $d$ is required to be an even integer $\ge \max\{2,\deg(f)\}$. The algorithm is implemented in a SAGE program developed by the first author. The bound obtained is typically not as good as the bound obtain...
The recycling for recovery and reuse of material and energy resources undoubtedly provides a subs... more The recycling for recovery and reuse of material and energy resources undoubtedly provides a substantial alternative supply of raw materials and reduces the dependence on virgin feedstock. The main objective of this study was to assess the potential of dry municipal solid waste recycling in Mashhad city, Iran. Several questionnaires were prepared and distributed among various branches of the municipality, related organizations and people. The total amount of solid waste generated in Mashhad in 2008 was 594 800 tons with per capita solid waste generation rate of 0.609 kg person À1 day À1 . Environmental educational programmes via mass media and direct education of civilians were implemented to publicize the advantages and necessity of recycling. The amount of recycled dry solid waste was increased from 2.42% of total dry solid waste (2588.36 ton year À1 ) in 1999 to 7.22% (10 165 ton year À1 ) in 2008. The most important fractions of recycled dry solid waste in Mashhad included paper and board (51.33%), stale bread (14.59%), glass (9.73%), ferrous metals (9.73%), plastic (9.73%), polyethylene terephthalate (2.62%) and non-ferrous metals (0.97%). It can be concluded that unfortunately the potential of dry solid waste recycling in Mashhad has not been considered properly and there is a great effort to be made in order to achieve the desired conditions of recycling.
We make use of a result of Hurwitz and Reznick [8] , and a consequence of this result due to Fida... more We make use of a result of Hurwitz and Reznick [8] , and a consequence of this result due to Fidalgo and Kovacec [5], to determine a new sufficient condition for a polynomial f ∈ R[X 1 , . . . , Xn] of even degree to be a sum of squares. This result generalizes a result of Lasserre in [10] and a result of Fidalgo and Kovacec in , and it also generalizes the improvements of these results given in . We apply this result to obtain a new lower bound fgp for f , and we explain how fgp can be computed using geometric programming. The lower bound fgp is generally not as good as the lower bound fsos introduced by Lasserre and Parrilo and Sturmfels , which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of fgp is much faster. The computation is simplest when the highest degree term of f has the form n i=1 a i X 2d i , a i > 0, i = 1, . . . , n. The lower bounds for f established in are obtained by evaluating the objective function of the geometric program at the appropriate feasible points.
Let $R$ be a unital algebra over reals and $K\subseteq Hom(R,\mathbb{R})$, closed with respect to... more Let $R$ be a unital algebra over reals and $K\subseteq Hom(R,\mathbb{R})$, closed with respect to the product topology. We consider $R$ endowed with the topology induced by the family of seminorms $\rho_{\alpha}(a):=|\alpha(a)|$, for $\alpha\in K$ and $a\in R$. In case $K$ is compact, we also consider the topology induced by $\|a\|_K:=\sup_{\alpha\in K}|\alpha(a)|$ for $a\in R$. If $K$ is Zariski dense, then those topologies are Hausdorff. In this paper we prove that the closure of the cone of sums of 2d-powers, with respect to those two topologies is equal to the cone $\{a\in R:\alpha(a)\ge0,\forall\alpha\in K\}$. In particular, any continuous linear functional $L$ on the polynomial ring $R=\mathbb{R}[X_1,...,X_n]$ with $L(h^{2d})\ge0$ for each polynomial $h$, is integration with respect to a positive Borel measure supported on $K$. We give necessary and sufficient conditions to ensure the continuity of a linear functional. We compare our results with results of Schm\"udgen, B...
ATP-sensitive K + (K ATP ) channels exist in many excitable cells, including cardiac myocytes, pa... more ATP-sensitive K + (K ATP ) channels exist in many excitable cells, including cardiac myocytes, pancreatic b cells, muscle cells, and neurons 1,2 and are involved in several physiological functions. 3,4 KATP channels are expressed pre-and post-synaptically in many brain regions. They open and close in response to changes in intracellular ATP/ADP ratios. Low ATP levels open these channels, allowing K + efflux and cell hyperpolarization. 5 Therefore, the activity of K ATP channels is regulated by cell metabolism and provides a means of linking the electrical activity of a cell to its metabolic state. Pharmacological studies have also demonstrated that K ATP channels play an important role in the control of seizure threshold in several in vitro and in vivo models. 3,7-12 Moreover, it has been shown that mice lacking a subunit of K ATP channels (Kir 6.2 À/À mice) are vulnerable to hypoxia, exhibiting a reduced threshold for generalized seizure. 9 Transgenic mice, overexpressing the sulfonylurea receptor (SUR1) gene in the forebrain, show a significant increase in the threshold for kainite-induced seizures. 13 Thus, physiopathologic conditions altering the K ATP activation could possibly affect the seizure threshold.
In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide... more In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide (NO) system on the antidepressant-like effects of paroxetine in the mouse forced swimming test. Swim sessions were conducted by placing mice in individual glass cylinders filled with water for 6 min. The duration of behavioral immobility during the last 4 min of the test was evaluated. Paroxetine (8 and 16 mg/kg, intraperitoneal [i.p.]) significantly reduced the immobility times of mice, whereas lower doses (2 and 4 mg/kg) had no effect. NMDA antagonists MK-801 (0.1 and 0.25 mg/kg, i.p.) and ifenprodil (1 and 3 mg/kg, i.p.) and the NO synthase inhibitor NG-L-arginine methyl ester (L-NAME; 30 and 100 mg/kg, i.p.) significantly decreased the immobility time. Lower doses of MK-801 (0.01 and 0.05 mg/kg), ifenprodil (0.1 and 0.5 mg/kg), and L-NAME (10 mg/kg) had no effect. Combined treatment of subeffective doses of paroxetine (4 mg/kg) and MK-801 (0.05 mg/kg), ifenprodil (0.5 mg/kg), and L-NAME (10 mg/kg) robustly exerted an antidepressant-like effect. The noneffective dose of a NO precursor L: -arginine (750 mg/kg, i.p.) prevented the antidepressant-like effect of paroxetine (30 mg/kg). We suggested, for the first time, a possible role for NMDAR/NO signaling in the antidepressant-like effects of paroxetine, providing a new approach for the treatment of depression.
The multivariate moment problem is investigated in the general context of the polynomial algebra ... more The multivariate moment problem is investigated in the general context of the polynomial algebra R[x i | i ∈ Ω] in an arbitrary number of variables x i , i ∈ Ω. The results obtained are sharpest when the index set Ω is countable. Extensions of Haviland's theorem [13] and Nussbaum's theorem [28] are proved. Lasserre's description of the support of the measure in terms of the non-negativity of the linear functional on a quadratic module of R[x i | i ∈ Ω] in [21] is shown to remain valid in this more general situation. The main tool used in the paper is an extension of the localization method developed by the third author in [24], [26] and [27]. Various results proved in [24], [26] and [27]
POSTERS or hydrophobic bile salts (GCDC). IGF1 isoforms were analyzed by realtime PCR by using b-... more POSTERS or hydrophobic bile salts (GCDC). IGF1 isoforms were analyzed by realtime PCR by using b-actin as internal reference. At least 3 different IGF1 isoforms were identified. In both hepatocytes and cholangiocytes, the "locally acting" IGF1 isoform (XO6108) and circulating IGF1 isoform (NM_178866) represented respectively 44% and 52% of the total IGF1. Basal mRNAs for both "locally acting" and circulating IGF1 isoform were 10-fold higher in hepatocytes than cholangiocytes. After BDL for 3 hrs, the "locally acting" IGF1 isoform decreased 3-fold in hepatocytes but remains stable in cholangiocytes (p < 0.05). After 1 week BDL, hepatocytes, which do not proliferate and show apoptotic damage, displayed a further 5-fold decrease of "locally acting" IGF1 mRNA. In contrast, cholangiocytes which markedly proliferate showed a 8-fold increase of the "locally acting" IGF1 mRNA. The effect of 3 hours BDL on IGF1 isoforms was reproduced in vitro by incubation with glycochenodeoxycholate (GCDC). The cytotoxic effects (inhibition of proliferation and induction of apoptosis) of GCDC on isolated cholangiocytes were enhanced by selective silencing (SiRNA) of "locally acting", IGF1 isoform into higher extent than silencing of circulating IGF1 isoform. Conclusions: rat hepatocytes and cholangiocytes express the "locally acting" IGF1 isoform which decreased during cell damage and increased during cell proliferation. The "locally acting" IGF1 was more active than the circulating isoform in protecting cholangiocytes from GCDC-induced apoptosis. These findings indicates that, other than in muscle and neural tissues, also in liver cells the "locally acting" IGF1 isoform may play a major role in modulating response to damage.
In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide... more In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide (NO) system on the antidepressant-like effects of paroxetine in the mouse forced swimming test. Swim sessions were conducted by placing mice in individual glass cylinders filled with water for 6 min. The duration of behavioral immobility during the last 4 min of the test was evaluated. Paroxetine (8 and 16 mg/kg, intraperitoneal [i.p.]) significantly reduced the immobility times of mice, whereas lower doses (2 and 4 mg/kg) had no effect. NMDA antagonists MK-801 (0.1 and 0.25 mg/kg, i.p.) and ifenprodil (1 and 3 mg/kg, i.p.) and the NO synthase inhibitor NG-L-arginine methyl ester (L-NAME; 30 and 100 mg/kg, i.p.) significantly decreased the immobility time. Lower doses of MK-801 (0.01 and 0.05 mg/kg), ifenprodil (0.1 and 0.5 mg/kg), and L-NAME (10 mg/kg) had no effect. Combined treatment of subeffective doses of paroxetine (4 mg/kg) and MK-801 (0.05 mg/kg), ifenprodil (0.5 mg/kg), and L-NAME (10 mg/kg) robustly exerted an antidepressant-like effect. The noneffective dose of a NO precursor L: -arginine (750 mg/kg, i.p.) prevented the antidepressant-like effect of paroxetine (30 mg/kg). We suggested, for the first time, a possible role for NMDAR/NO signaling in the antidepressant-like effects of paroxetine, providing a new approach for the treatment of depression.
Let V be the countable dimensional polynomial R-algebra R[X] := R[X1, . . . , Xn]. Let τ be a loc... more Let V be the countable dimensional polynomial R-algebra R[X] := R[X1, . . . , Xn]. Let τ be a locally convex topology on V. Let K be a closed subset of R n , and let M := M {g 1 ,···gs} be a finitely generated quadratic module in V . We investigate the following question: When is the cone Psd(K) (of polynomials nonnegative on K) included in the closure of M ? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of M = R[X] 2 with respect to weighted norm-p topologies. We show that this closure coincides with the cone Psd(K) where K is a certain convex compact polyhedron. We use these results to generalize Berg's et al work on exponentially bounded moment sequences.
In [3] Berg, Christensen and Ressel prove that the closure of the cone of sums of squares R[X] 2 ... more In [3] Berg, Christensen and Ressel prove that the closure of the cone of sums of squares R[X] 2 in the polynomial ring R[X] := R[X 1 , . . . , Xn] in the topology induced by the 1 -norm is equal to Pos([−1, 1] n ), the cone consisting of all polynomials which are non-negative on the hypercube [−1, 1] n .
The purpose of this study was to investigate the effect of the endogenous cannabinoid anandamide ... more The purpose of this study was to investigate the effect of the endogenous cannabinoid anandamide on the nonadrenergic noncholinergic (NANC) relaxant responses to electrical field stimulation in isolated rat corpus cavernosum. The corporal strips were mounted under tension in a standard oxygenated organ bath with guanethidine sulfate (5 μM) and atropine (1 μM) (to produce adrenergic and cholinergic blockade). The strips were precontracted with phenylephrine hydrochloride (7.5 μM) and electrical field stimulation was applied at different frequencies to obtain NANC-mediated relaxation. The expression of CB 1 , CB 2 and vanilloid receptor proteins within the rat corpus cavernosum was evaluated using western blot analysis. The results showed that the relaxant responses to electrical stimulation were significantly enhanced in the presence of anandamide at 1 and 3 μM. The potentiating effect of anandamide (1 μM) on relaxation responses was significantly attenuated by either the selective cannabinoid CB 1 receptor antagonist N-(piperidin-1-yl)-5-(4-iodophenyl)-1-(2, 4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide (AM251; 1 μM) or the vanilloid receptor antagonist capsazepine (3 μM), but not by the selective cannabinoid CB 2 receptor antagonist 6-iodo-2methyl-1-[2-(4-morpholinyl) ethyl]-1H-indol-3-yl (4-methoxyphenyl)methanone (AM630; 1 μM). Neither of these antagonists had influence on relaxation responses. Indomethacin (20 μM) had no effect on NANC-mediated relaxation in the presence or absence of anandamide (1 μM). Preincubation with N w -Nitro-L-Arginine Methyl Ester (L-NAME; 1 μM) significantly inhibited the relaxation responses in the presence or absence of 1 μM anandamide. Although at 30 nM, L-NAME did not cause a significant inhibition of relaxant responses individually, it significantly inhibited the potentiating effect of anandamide (1 μM) on relaxation responses. Anandamide (1 μM) had no influence on concentration-dependent relaxant responses to sodium nitroprusside (10 nM-1 mM), a nitric oxide (NO) donor. The western blotting of corporal tissues demonstrated the existence of both vanilloid and CB 1 receptors in corporal strips. In conclusion, our results showed that anandamide has a potentiating effect on NANC-mediated relaxation of rat corpus cavernosum through both CB 1 and vanilloid receptors and the NO-mediated component of the NANC relaxant responses to electrical stimulation is involved in this enhancement.
We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo a... more We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points.
Background/Aims: The clinical relevance of QT prolongation, the most widely recognized cardiac el... more Background/Aims: The clinical relevance of QT prolongation, the most widely recognized cardiac electrophysiological abnormality of cirrhosis, is still undefined. The aim of this study is to examine the susceptibility of chronic (4-week) bile duct-ligated rats to epinephrine-induced arrhythmias. The roles of nitric oxide and endogenous opioids were also evaluated.
Berg, Christensen and Ressel prove that the closure of the cone of sums of squares in the ring of... more Berg, Christensen and Ressel prove that the closure of the cone of sums of squares in the ring of real polynomials in the topology induced by the $\ell_1$-norm is equal to the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$. The result is deduced as a corollary of a general result which is valid for any commutative semigroup. In later work Berg and Maserick and also Berg, Christensen and Ressel establish an even more general result, for a commutative semigroup with involution, for the closure of the cone of sums of squares of symmetric elements in the weighted $\ell_1$-seminorm topology associated to an absolute value. In the present paper we give a new proof of these results which is based on Jacobi's representation theorem. At the same time, we use Jacobi's representation theorem to extend these results from sums of squares to sums of 2d-powers, proving, in particular, that for any integer $d>0$, the closure of the cone of sums of 2d-powers in the ring of real polynomials in the topology induced by the $\ell_1$-norm is equal the cone consisting of all polynomials which are non-negative on the hypercube $[-1,1]^n$.
Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which sa... more Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which satisfies $\rho(ab)\leq\rho(a)\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$ in the topology induced by $\rho$, for any integer $d\ge1$. We show that this closure is exactly the set of all elements $a\in A$ such that $\alpha(a)\ge0$ for every $\rho$-continuous $\mathbb{R}$-algebra homomorphism $\alpha : A \rightarrow \mathbb{R}$ with $\alpha(S)\subseteq[0,\infty)$, and that this result continues to hold when $\rho$ is replaced by any locally multiplicatively convex topology $\tau$ on $A$. We obtain a representation of any linear functional $L : A \rightarrow \reals$ which is continuous with respect to any such $\rho$ or $\tau$ and non-negative on $S$ as integration with respect to a unique Radon measure on the space of all real valued $\reals$-algebra homomorphisms on $A$, and we characterize the support of the measure obtained in this way.
Let $f,g_1,\dots,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,\dots,x_n]$. The paper d... more Let $f,g_1,\dots,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,\dots,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,\dots,m$. The paper shows that there is an algorithm for computing such a lower bound, based on geometric programming, which applies in a large number of cases. For example, the algorithm computes a lower bound for $f$ on a hypercube $\prod_{i=1}^n [-N_i,N_i]$, or, more generally, on any product of hyperellipsoids of a suitable form. The algorithm extends and generalizes earlier algorithms of Ghasemi and Marshall, dealing with the case $m=0$, and of Ghasemi, Lasserre and Marshall, dealing with the case $m=1$ and $g_1= M-(x_1^d+\dots+x_n^d)$. Here, $d$ is required to be an even integer $\ge \max\{2,\deg(f)\}$. The algorithm is implemented in a SAGE program developed by the first author. The bound obtained is typically not as good as the bound obtain...
The recycling for recovery and reuse of material and energy resources undoubtedly provides a subs... more The recycling for recovery and reuse of material and energy resources undoubtedly provides a substantial alternative supply of raw materials and reduces the dependence on virgin feedstock. The main objective of this study was to assess the potential of dry municipal solid waste recycling in Mashhad city, Iran. Several questionnaires were prepared and distributed among various branches of the municipality, related organizations and people. The total amount of solid waste generated in Mashhad in 2008 was 594 800 tons with per capita solid waste generation rate of 0.609 kg person À1 day À1 . Environmental educational programmes via mass media and direct education of civilians were implemented to publicize the advantages and necessity of recycling. The amount of recycled dry solid waste was increased from 2.42% of total dry solid waste (2588.36 ton year À1 ) in 1999 to 7.22% (10 165 ton year À1 ) in 2008. The most important fractions of recycled dry solid waste in Mashhad included paper and board (51.33%), stale bread (14.59%), glass (9.73%), ferrous metals (9.73%), plastic (9.73%), polyethylene terephthalate (2.62%) and non-ferrous metals (0.97%). It can be concluded that unfortunately the potential of dry solid waste recycling in Mashhad has not been considered properly and there is a great effort to be made in order to achieve the desired conditions of recycling.
We make use of a result of Hurwitz and Reznick [8] , and a consequence of this result due to Fida... more We make use of a result of Hurwitz and Reznick [8] , and a consequence of this result due to Fidalgo and Kovacec [5], to determine a new sufficient condition for a polynomial f ∈ R[X 1 , . . . , Xn] of even degree to be a sum of squares. This result generalizes a result of Lasserre in [10] and a result of Fidalgo and Kovacec in , and it also generalizes the improvements of these results given in . We apply this result to obtain a new lower bound fgp for f , and we explain how fgp can be computed using geometric programming. The lower bound fgp is generally not as good as the lower bound fsos introduced by Lasserre and Parrilo and Sturmfels , which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of fgp is much faster. The computation is simplest when the highest degree term of f has the form n i=1 a i X 2d i , a i > 0, i = 1, . . . , n. The lower bounds for f established in are obtained by evaluating the objective function of the geometric program at the appropriate feasible points.
Let $R$ be a unital algebra over reals and $K\subseteq Hom(R,\mathbb{R})$, closed with respect to... more Let $R$ be a unital algebra over reals and $K\subseteq Hom(R,\mathbb{R})$, closed with respect to the product topology. We consider $R$ endowed with the topology induced by the family of seminorms $\rho_{\alpha}(a):=|\alpha(a)|$, for $\alpha\in K$ and $a\in R$. In case $K$ is compact, we also consider the topology induced by $\|a\|_K:=\sup_{\alpha\in K}|\alpha(a)|$ for $a\in R$. If $K$ is Zariski dense, then those topologies are Hausdorff. In this paper we prove that the closure of the cone of sums of 2d-powers, with respect to those two topologies is equal to the cone $\{a\in R:\alpha(a)\ge0,\forall\alpha\in K\}$. In particular, any continuous linear functional $L$ on the polynomial ring $R=\mathbb{R}[X_1,...,X_n]$ with $L(h^{2d})\ge0$ for each polynomial $h$, is integration with respect to a positive Borel measure supported on $K$. We give necessary and sufficient conditions to ensure the continuity of a linear functional. We compare our results with results of Schm\"udgen, B...
ATP-sensitive K + (K ATP ) channels exist in many excitable cells, including cardiac myocytes, pa... more ATP-sensitive K + (K ATP ) channels exist in many excitable cells, including cardiac myocytes, pancreatic b cells, muscle cells, and neurons 1,2 and are involved in several physiological functions. 3,4 KATP channels are expressed pre-and post-synaptically in many brain regions. They open and close in response to changes in intracellular ATP/ADP ratios. Low ATP levels open these channels, allowing K + efflux and cell hyperpolarization. 5 Therefore, the activity of K ATP channels is regulated by cell metabolism and provides a means of linking the electrical activity of a cell to its metabolic state. Pharmacological studies have also demonstrated that K ATP channels play an important role in the control of seizure threshold in several in vitro and in vivo models. 3,7-12 Moreover, it has been shown that mice lacking a subunit of K ATP channels (Kir 6.2 À/À mice) are vulnerable to hypoxia, exhibiting a reduced threshold for generalized seizure. 9 Transgenic mice, overexpressing the sulfonylurea receptor (SUR1) gene in the forebrain, show a significant increase in the threshold for kainite-induced seizures. 13 Thus, physiopathologic conditions altering the K ATP activation could possibly affect the seizure threshold.
In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide... more In this study, we evaluated the involvement of N-methyl-D-aspartate receptor (NMDAR)/nitric oxide (NO) system on the antidepressant-like effects of paroxetine in the mouse forced swimming test. Swim sessions were conducted by placing mice in individual glass cylinders filled with water for 6 min. The duration of behavioral immobility during the last 4 min of the test was evaluated. Paroxetine (8 and 16 mg/kg, intraperitoneal [i.p.]) significantly reduced the immobility times of mice, whereas lower doses (2 and 4 mg/kg) had no effect. NMDA antagonists MK-801 (0.1 and 0.25 mg/kg, i.p.) and ifenprodil (1 and 3 mg/kg, i.p.) and the NO synthase inhibitor NG-L-arginine methyl ester (L-NAME; 30 and 100 mg/kg, i.p.) significantly decreased the immobility time. Lower doses of MK-801 (0.01 and 0.05 mg/kg), ifenprodil (0.1 and 0.5 mg/kg), and L-NAME (10 mg/kg) had no effect. Combined treatment of subeffective doses of paroxetine (4 mg/kg) and MK-801 (0.05 mg/kg), ifenprodil (0.5 mg/kg), and L-NAME (10 mg/kg) robustly exerted an antidepressant-like effect. The noneffective dose of a NO precursor L: -arginine (750 mg/kg, i.p.) prevented the antidepressant-like effect of paroxetine (30 mg/kg). We suggested, for the first time, a possible role for NMDAR/NO signaling in the antidepressant-like effects of paroxetine, providing a new approach for the treatment of depression.
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Papers by Mehdi Ghasemi