Generalizations of Weighted Trapezoidal Inequality for Monotonic Mappings and Its Applications

In this paper, we establish some generalizations of weighted trapezoid inequality for monotonic mappings, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping

Structure and Reactivity Studies of Bis(pyridylimino)isoindolate Transition Metal Complexes.

In this dissertation, transition metal complexes supported by bpi-type (bpi = 1,3-bis(2’-pyridylimino)isoindolate) ligands were designed and synthesized to study their activity, selectivity, and stability in hydrogenation and dehydrogenation reactions and to determine the role of the bpi ligand in these transformations. A new family of ruthenium bpi complexes capable of catalyzing promoterless and chemoselective dehydrogenation of alcohols and amines with liberation of dihydrogen were developed. In particular, the bis(phosphine) ruthenium bMepi hydride (bMepi = 1,3-bis(6’-methyl-2’-pyridylimino)isoindolate) system mediates dehydrogenation of secondary alcohols to ketones, dehydrogenative coupling of primary alcohols to esters, and double dehydrogenation of primary amines to nitriles with high conversion efficiency. An unusual feature of this catalyst system is the high selectivity for secondary alcohol dehydrogenation in the presence of primary alcohols. By avoiding the use of hazardous reagents and harsh oxidants, these dehydrogenative transformations provide environmentally benign methodologies for fine and commodity chemical synthesis with high atom economy. Furthermore, to understand the relationship between catalyst structure and reactivity, the catalytic mechanism of acceptorless alcohol dehydrogenation was elucidated by a series of kinetic and isotopic labeling studies, isolation of intermediates, and evaluation of new ligand variants. The new chemical knowledge acquired in the mechanistic investigation was applied to conceptualize and develop three new projects: (1) iron bMepi systems that feature control over catalytic alkene hydroboration activity and regioselectivity by remote site modifications, (2) ruthenium bpi complexes capable of upgrading ethanol to 1-butanol with state-of-the-art activity (53% conversion and 265 turnovers per hour), and (3) a new series of multifunctional ruthenium complexes with appended Lewis acidic borane sites for studying how Lewis acidity influences the reactivity of the ruthenium hydride moiety and biases the system for stereoselective semi-hydrogenation of alkynes. Collectively, the studies presented in this dissertation demonstrate the new development of highly active and chemoselective catalysts capable of promoting challenging dehydrogenation reactions and showcase how precise structural, electronic, and cooperative interactions in the secondary coordination environment can be used to regulate metal-based catalysis.PhDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120813/1/kueinin_1.pd

Association of Cannabis Use during Adolescence, Prefrontal CB1 Receptor Signaling, and Schizophrenia

The cannabinoid receptor 1 (CB1R) is the G-protein coupled receptor responsible for the majority of the endocannabinoid signaling in the human brain. It is widely distributed in the limbic system, basal ganglia, and cerebellum, which are areas responsible for cognition, memory, and motor control. Because of this widespread distribution, it is not surprising that drugs that activate CB1R have expected behavioral outcomes consistent with dysregulated signaling from these areas (e.g., memory loss, cognitive deficits, etc). In the context of this review, we present evidence for the role of CB1R signaling in the prefrontal cortex (PFC), an area involved in executive functions, with emphasis on the developmental regulation of CB1R signaling in the acquisition of mature PFC function. We further hypothesize how alterations in CB1R signaling specifically during adolescent maturation might confer liability to psychiatric disorders

Some New Discrete Inequalities of Opial and Lasota's Type

In this paper, we establish some new discrete inequalities of Opial and Lasota's type which reduce to some inequalities in [4]

Calcium-permeable AMPA receptors in the VTA and nucleus accumbens after cocaine exposure: when, how, and why?

In animal models of drug addiction, cocaine exposure has been shown to increase levels of calcium-permeable AMPA receptors (CP-AMPARs) in two brain regions that are critical for motivation and reward—the ventral tegmental area (VTA) and the nucleus accumbens (NAc). This review compares CP-AMPAR plasticity in the two brain regions and addresses its functional significance. In VTA dopamine neurons, cocaine exposure results in synaptic insertion of high conductance CP-AMPARs in exchange for lower conductance calcium-impermeable AMPARs (CI-AMPARs). This plasticity is rapid in onset (hours), GluA2-dependent, and can be observed with a single cocaine injection. Whereas it is short-lived after experimenter-administered cocaine, it persists for months after cocaine self-administration. In addition to strengthening synapses and altering Ca2+ signaling, CP-AMPAR insertion alters subsequent induction of plasticity at VTA synapses. However, CP-AMPAR insertion is unlikely to mediate the increased DA cell activity that occurs during early withdrawal from cocaine exposure. Metabotropic glutamate receptor 1 (mGluR1) exerts a negative influence on CP-AMPAR accumulation in the VTA. Acutely, mGluR1 stimulation elicits a form of LTD resulting from CP-AMPAR removal and CI-AMPAR insertion. In medium spiny neurons (MSNs) of the NAc, extended access cocaine self-administration is required to increase CP-AMPAR levels. This is first detected after approximately a month of withdrawal and then persists. Once present in NAc synapses, CP-AMPARs mediate the expression of incubation of cue-induced cocaine craving. The mechanism of their accumulation may be GluA1-dependent, which differs from that observed in the VTA. However, similar to VTA, mGluR1 stimulation removes CP-AMPARs from MSN synapses. Loss of mGluR1 tone during cocaine withdrawal may contribute to CP-AMPAR accumulation in the NAc. Thus, results in both brain regions point to the possibility of using positive modulators of mGluR1 as treatments for cocaine addiction

Nitric Oxide–Soluble Guanylyl Cyclase–Cyclic GMP Signaling in the Striatum: New Targets for the Treatment of Parkinson's Disease?

Striatal nitric oxide (NO)-producing interneurons play an important role in the regulation of corticostriatal synaptic transmission and motor behavior. Striatal NO synthesis is driven by concurrent activation of NMDA and dopamine (DA) D1 receptors. NO diffuses into the dendrites of medium-sized spiny neurons which contain high levels of NO receptors called soluble guanylyl cyclases (sGC). NO-mediated activation of sGC leads to the synthesis of the second messenger cGMP. In the intact striatum, transient elevations in intracellular cGMP primarily act to increase neuronal excitability and to facilitate glutamatergic corticostriatal transmission. NO–cGMP signaling also functionally opposes the inhibitory effects of DA D2 receptor activation on corticostriatal transmission. Not surprisingly, abnormal striatal NO–sGC–cGMP signaling becomes apparent following striatal DA depletion, an alteration thought to contribute to pathophysiological changes observed in basal ganglia circuits in Parkinson's disease (PD). Here, we discuss recent developments in the field which have shed light on the role of NO–sGC–cGMP signaling pathways in basal ganglia dysfunction and motor symptoms associated with PD and l-DOPA-induced dyskinesias

CB1 Cannabinoid Receptor Expression in the Striatum: Association with Corticostriatal Circuits and Developmental Regulation

Corticostriatal circuits mediate various aspects of goal-directed behavior and are critically important for basal ganglia-related disorders. Activity in these circuits is regulated by the endocannabinoid system via stimulation of CB1 cannabinoid receptors. CB1 receptors are highly expressed in projection neurons and select interneurons of the striatum, but expression levels vary considerably between different striatal regions (functional domains). We investigated CB1 receptor expression within specific corticostriatal circuits by mapping CB1 mRNA levels in striatal sectors defined by their cortical inputs in rats. We also assessed changes in CB1 expression in the striatum during development. Our results show that CB1 expression is highest in juveniles (P25) and then progressively decreases toward adolescent (P40) and adult (P70) levels. At every age, CB1 receptors are predominantly expressed in sensorimotor striatal sectors, with considerably lower expression in associative and limbic sectors. Moreover, for most corticostriatal circuits there is an inverse relationship between cortical and striatal expression levels. Thus, striatal sectors with high CB1 expression (sensorimotor sectors) tend to receive inputs from cortical areas with low expression, while striatal sectors with low expression (associative/limbic sectors) receive inputs from cortical regions with higher expression (medial prefrontal cortex). In so far as CB1 mRNA levels reflect receptor function, our findings suggest differential CB1 signaling between different developmental stages and between sensorimotor and associative/limbic circuits. The regional distribution of CB1 receptor expression in the striatum further suggests that, in sensorimotor sectors, CB1 receptors mostly regulate GABA inputs from local axon collaterals of projection neurons, whereas in associative/limbic sectors, CB1 regulation of GABA inputs from interneurons and glutamate inputs may be more important