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Algebraic operations on generalized hesitant fuzzy numbers are key tools to address the problems with decision uncertainty. In this paper, by studying the arithmetic operations on generalized trapezoidal hesitant fuzzy numbers, modified arithmetic operations are introduced for this class of numbers so that, using these arithmetic operations, the multiplication and division of two generalized trapezoidal hesitant fuzzy numbers are always generalized trapezoidal hesitant fuzzy numbers. Furthermore, a generalized trapezoidal hesitant fuzzy number raised to the power of a real number is a generalized trapezoidal hesitant fuzzy number, and in the defined division, the case where the denominator becomes zero is not considered. Numerical examples are used to show the shortcomings of the previous arithmetic operations as well as the efficiencies of the arithmetic operations proposed in this research for generalized trapezoidal hesitant fuzzy numbers. Finally, the application of the proposed new arithmetic operations to generalized trapezoidal hesitant fuzzy numbers in solving the generalized trapezoidal hesitant fully fuzzy equation is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new method for solving fuzzy Bernoulli differential equation (FBDE) under generalized differentiability. At the beginning, by stating the theorems, we define nth power of LR fuzzy function and the derivative of LR fuzzy function. Then, we obtain core function to determine LR fuzzy solution, through solving 1-cut FBDE, and calculate spread functions by finding the sign of real valued functions of coefficients of FBDE and finding the sign of core function. Also, numerical examples are presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Since complex interval matrix have many applications in different fields of science, in this paper interval complex matrix system as [W][Z] = [K] in which [W]; [K] are n × n known interval complex matrices and [Z] is n × n unknown interval complex matrix is studied. Using operations on interval complex numbers and matrices and defining a theorem, two auxiliary addition and subtraction complex systems are introduced and proved. Then, using the equality property of two complex numbers, the auxiliary interval complex systems are transformed to real crisp systems. Then the new system is solved and [Z] is achieved. Finally, some numerical examples are given to illustrate the applicability and ability of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy dual matrix system as à + ... = ... ... + ... in which Ã; ...; ...; ...; ... are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective function. We prove some theorems and we suggest conditions in which the fuzzy dual matrix system of à ... + ... = ... ... + ... and the fuzzy matrix system of (à #920;H ...) ... = ( ... ΘH eB) have the same LR fuzzy solution and we discuss about the conditions where LR fuzzy dual matrix system has crisp solution. Finally numerical examples are solved to illustrate the ability, accuracy and capability of the proposed method. [ABSTRACT FROM AUTHOR]

Objective:Despite the important role of α2-adrenoceptors in pain modulation processes, the impact of administration of α2-adrenoceptor agonist and antagonist on the density of hippocampal α2-adrenoceptor-immunoreactive neurons has not been investigated. Therefore, we aimed to determine the effect of single doses of clonidine and yohimbine on the density of α2-adrenoceptor-immunoreactive neurons in rat hippocampus. Materials and Methods:Adult male Wistar rats received a single dose of clonidine (0.7 mg/kg) alone or 5 min after intraperitoneal (1 mg/kg) and/or intracerebroventricular (5 µg/kg) injection of yohimbine. After histological processing, neurons with α2-adrenoceptor immunoreactivity were identified and counted through immunohistochemical analysis of hippocampal regions. Results:Clonidine slightly increased the number of α2-adrenoceptor-immunoreactive neurons in the hippocampal subregions compared with the normal saline group. Intraperitoneal injection of yohimbine followed by injection of clonidine significantly increased the number of α2-adrenoceptor-immunoreactive neurons in subregions cornu ammonis 1 (CA1) and cornu ammonis 3 (CA3). Intracerebroventricular injection of yohimbine after injection of clonidine significantly reduced the number of α2-adrenoceptor-immunoreactive neurons in all hippocampal subregions. Conclusion:The present study demonstrates that intraperitoneal administration of α2-adrenoceptor agonist clonidine increases the density of α2-adrenoceptor-immunoreactive neurons in rat hippocampus, while intracerebroventricular injection of yohimbine decreases the density of these neurons. [ABSTRACT FROM AUTHOR]

In this paper, fuzzy linear system as $$\widetilde{A} \widetilde{X}+ \widetilde{B} \widetilde{X}=\widetilde{Y}$$ in which $$\widetilde{A}, \widetilde{B}$$ are $$n \times n$$ fuzzy matrices and $$\widetilde{X}, \widetilde{Y}$$ are $$n \times 1$$ fuzzy vectors is studied. A new method to solve such systems based on interval linear system, interval inclusion linear system is proposed. Numerical examples are given to illustrate the ability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy dual matrix system as Ax̃ + B̃ = Cx̃ + D̃ in which A, C are n × n crisp matrices and B̃, D̃ are n × n LR fuzzy matrices is studied. To obtain the solution of fuzzy dual system, we initially solve 1-cut and use minimization problem to calculate the spreads. Afterwards, we explain the relationship between the solutions of the systems of Ax̃ + B̃ = Cx̃ + D̃ and (A - C)x̃ = (D̃ ⊖h B̃). Finally, some examples are solved to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Objectives: Amyloid β plaques, in Alzheimer's disease, are deposits in different areas of the brain such as prefrontal cortex, molecular layer of the cerebellum, and the hippocampal formation. Amyloid β aggregates lead to the release of cytochrome c and finally neuronal cell death in brain tissue. hCG has critical roles in brain development, neuron differentiation, and function. Therefore, we investigated the effect of hCG on the density of the congophilic Aβ plaque and cytochrome c-ir neurons in the hippocampus, prefrontal cortex, and cerebellum of Streptozotocin (STZ)-treated rats., Materials and Methods: Alzheimer model in rats (except the control group) was induced by streptozotocin (3 mg/kg, Intracerebroventricularly (ICV)). Experimental group rats received streptozotocin and then different doses of hCG (50, 100, and 200 IU, intraperitoneally) for 3 days. 48 hr after last drug injection and after histological processing, the brain sections were stained by congo red for congophilic amyloid β plaques and cytochrome c in the hippocampus, prefrontal cortex, and cerebellum were immunohistochemically stained., Results: Density of congophilic Aβ plaques and cytochrome c-immunoreactive neurons was significantly higher in ICV STZ treated rats than controls. Treatment with three doses of hCG significantly decreased the density of congophilic Aβ plaques and cytochrome c-immunoreactive neurons in the rat hippocampus, prefrontal cortex, and cerebellum in ICV STZ-treated rats ( P <0.05)., Conclusion: hCG can be useful in AD patients to prevent the congophilic Aβ plaque formation and decrease cytochrome c-immunoreactive neuron density in the brain., Competing Interests: All authors declare that there are no conflicts of interest.

The hippocampus is important for learning tasks, such as conditioned place preference (CPP), which is widely used as a model for studying the reinforcing effects of drugs with dependence liability. Long-term opiate use may produce maladaptive plasticity in the brain structures involved in learning and memory, such as the hippocampus. We investigated the phenomenon of conditioning with morphine on the cell density of female rat hippocampus. Forty-eight female Wistar rats weighing on average 200-250 g were used. Rats were distributed into eight groups. Experimental groups received morphine daily (three days) at different doses (2.5, 5, 7.5 mg/kg) and the control-saline group received normal saline (1 ml/kg), and then the CPP test was performed. Three sham groups received only different doses (2.5, 5, 7.5 mg/kg) of morphine without CPP test. Forty-eight hours after behavioural testing animals were decapitated under chloroform anaesthesia and their brains were fixed, and after tissue processing, slices were stained with cresyl violet for neurons and phosphotungstic acid haematoxylin for astrocytes. The maximum response was obtained with 5 mg/kg of morphine. The density of neurons in CA1 and CA3 areas of hippocampus after injection of morphine and CPP was decreased. The number of astrocytes in different areas of hippocampus was increased after injection of morphine and CPP. It seems that the effective dose was 5 mg/kg, as it led to the CPP. We concluded that both injection of mor phine and CPP can decrease the density of neurons and also increase the number of astrocytes in the rat hippocampus.

Introduction: MDMA or ecstasy is a derivative of amphetamines used mostly by young people worldwide. Although the acute effects of this drug are known, the effect of chronic administration is not well studied. Therefor the aim of this study was to determine the effects of repeated (long term) administration of MDMA on rats' memory and their hippocampal cell density., Method: Young adult male Wistar rats 200 ± 20 g served as subjects. The rats were randomly distributed into three MDMA treated groups (3×2.5 mg/kg, 3×5 mg/kg, 3×10 mg/kg) and one control-saline group. All animals received MDMA intraperitoneally (3h apart; a challenge) 7th day of every week for consecutive 4 weeks. Animals were trained before and were tested after injections for their memory status using the standards passive avoidance method. Finally, 24hr after the memory test, rats were sacrificed and after tissue operations, the hippocampal astrocytes and neurons were counted., Results: Results showed that the number of neurons in all experimental groups was lower than the control-saline group. The most decreased number of neurons was shown in 5 mg/kg MDMA group compared to control-saline in all the regions of hippocampus. Also we found that repeated administration of MDMA reduced the number of hippocampal astrocytes., Discussion: It is concluded that repeated administration of MDMA can reduce density of neurons and astrocytes and this decrease is not dose dependence.

Apoptosis, known as programmed cell death, plays a crucial role in normal development and tissue homeostasis. Apoptosis is also involved in neurodegenerative diseases such as Alzheimer's disease. Amnesia refers to the loss of memory and can also be a warning sign of neurodegenerative diseases. The antioxidant properties of Ginkgo biloba extract was known previously. Therefore, the aim of this study was to examine the effects of Ginkgo biloba extract on the rat's hippocampal apoptotic neurons number after Scopolamine based amnesia. Thirty-six adult male Wistar rats were used. Rats were randomly divided into control, sham, protective and treatment groups. The rats in the sham group received only scopolamine hydrobromide (3 mg/kg) intraperitoneally. The rats in the protective and treatment groups received Ginkgo biloba extract (40, 80 mg/kg) for 7 days intraperitoneally before/after scopolamine injection. Then 48 h after the last injection, the brains of rats were withdrawn and fixed with paraformaldehyde, and then, after histological processing, the slices were stained with the TUNEL kit for apoptotic neurons. Data were compared by the ANOVA Post Hoc Tukey test; P < 0.05 was considered significant. Our results showed that Scopolamine (in the sham group) increased significantly the number of apoptotic neurons in all areas of the hippocampus compared with the control. Whereas, Ginkgo biloba extract reduce the neuronal apoptosis in the hippocampus before and/or after encounter with scopolamine. We concluded that pretreatment and treatment injection of Ginkgo biloba extract can have a protective effect for neurons and it can limit apoptosis in all area of the hippocampus.