Stability of a functional equation deriving from cubic and quartic functions

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation &4(f(3x+y)+f(3x-y))=-12(f(x+y)+f(x-y)) &+12(f(2x+y)+f(2x-y))-8f(y)-192f(x)+f(2y)+30f(2x)

On the Lp-spaces techniques in the existence and uniqueness of the fuzzy fractional Korteweg-de Vries equation’s solution

In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented

On the stability of J∗−^*-derivations

In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J^*-$derivations by using the fixed point alternative

Nearly Jordan -Homomorphisms between Unital -Algebras

Let , be two unital ∗-algebras. We prove that every almost unital almost linear mapping ℎ : → which satisfies ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) for all ∈(), all ∈, and all =0,1,2,…, is a Jordan homomorphism. Also, for a unital ∗-algebra of real rank zero, every almost unital almost linear continuous mapping ℎ∶→ is a Jordan homomorphism when ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) holds for all ∈1 (sa), all ∈, and all =0,1,2,…. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan ∗-homomorphisms between unital ∗-algebras by using the fixed points methods

Targeting bone marrow to potentiate the anti-tumor effect of tyrosine kinase inhibitor in preclinical rat model of human glioblastoma

Antiangiogenic agents caused paradoxical increase in pro-growth and pro-angiogenic factors and caused tumor growth in glioblastoma (GBM). It is hypothesized that paradoxical increase in pro-angiogenic factors would mobilize Bone Marrow Derived Cells (BMDCs) to the treated tumor and cause refractory tumor growth. The purposes of the studies were to determine whether whole body irradiation (WBIR) or a CXCR4 antagonist (AMD3100) will potentiate the effect of vatalanib (a VEGFR2 tyrosine kinase inhibitor) and prevent the refractory growth of GBM. Human GBM were grown orthotopically in three groups of rats (control, pretreated with WBIR and AMD3100) and randomly selected for vehicle or vatalanib treatments for 2 weeks. Then all animals underwent Magnetic Resonance Imaging (MRI) followed by euthanasia and histochemical analysis. Tumor volume and different vascular parameters (plasma volume (vp), forward transfer constant (Ktrans), back flow constant (kep), extravascular extracellular space volume (ve) were determined from MRI. In control group, vatalanib treatment increased the tumor growth significantly compared to that of vehicle treatment but by preventing the mobilization of BMDCs and interaction of CXCR4-SDF-1 using WBIR and ADM3100, respectively, paradoxical growth of tumor was controlled. Pretreatment with WBIR or AMD3100 also decreased tumor cell migration, despite the fact that ADM3100 increased the accumulation of M1 and M2 macrophages in the tumors. Vatalanib also increased Ktrans and ve in control animals but both of the vascular parameters were decreased when the animals were pretreated with WBIR and AMD3100. In conclusion, depleting bone marrow cells or CXCR4 interaction can potentiate the effect of vatalanib

Measurement of rat brain tumor kinetics using an intravascular MR contrast agent and DCE‐MRI nested model selection

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109323/1/jmri24469.pd