Abstract:
A previously healthy 26 years old right-handed mansustained a penetrating brain injury (PBI) from gunshotwound to the head. The bullet entered the right parietooccipitaljunction, traveled diagonally through the occipitalpole and ended in the left fronto-temporal lobe. Hedeveloped right hemiparesis and global aphasia. He wasenrolled in speech therapy (ST), and was started onlevetiracetam (LEV) 500 mg twice daily (BID) for seizureprophylaxis, then LEV was increased to 750mg BID.After 8 days on LEV 750 mg BID the patient pronouncedthe names of his children and answered questionsappropriately with verbal “yes” and “no”. At discharge,FIM scores in comprehension, expression, memory, andsocial interaction had all improved from 2 to 4. He wasable to respond verbally at the 1-3 word level with 50%accuracy and had shown improvement in auditorycomprehension and verbal expression. The patient waskept on LEV 750 mg BID for 7 months. He had 50outpatient ST sessions. At 9 months, he was able to reada paragraph he had written, and used a paper guide toscan lines. His comprehension of the written languageimproved to the sentence level, and his moneymanagement skills improved to modified independent.Conclusions: LEV appears to improve aphasia andcognitive outcomes of PBI patients treated with ST. Largeprospective randomized trials are needed to confirm thisclinical observation and to establish treatment protocolsfor PBI-induced aphasia that will incorporate ST and LEV.

Abstract:
A 50 year-old male with a history of atrial fibrillation onCoumadin developed an acute infarct of the right MiddleCerebral Artery (MCA) involving the frontal and temporallobes. The patient developed cerebral edema with amidline shift and hemorrhagic conversion. Aventriculostomy was performed followed by an emergentfrontotemporal decompressive craniotomy. The patientdeveloped uncal herniation and underwent a redofrontotemporal craniectomy with right temporallobectomy and decompression of midbrain withevacuation of the basal ganglia hematoma. On admissionto an inpatient rehabilitation unit, approximately 20 monthsafter onset of injury, the patient was found to have diffusespasticity with multiple severe contractures, limited rangeof motion, hemifacial spasms, bruxism and cervicalmuscle dystonia. Patient had limited opening of his mouthboth actively and passively, work up revealed matureheterotopic ossification (HO) of the lefttemporomandibular joint (TMJ) at the condyloid processat the level of the condyloid head and neck of themandible.

Abstract:
Let K be a field and let m_0,...,m_{n} be an almost arithmetic sequence of positive integers. Let C be a toric variety in the affine (n+1)-space, defined parametrically by x_0=t^{m_0},...,x_{n}=t^{m_{n}}. In this paper we produce a minimal Gr\"obner basis for the toric ideal which is the defining ideal of C and give sufficient and necessary conditions for this basis to be the reduced Gr\"obner basis of C, correcting a previous work of \cite{Sen} and giving a much simpler proof than that of \cite{Ayy}.

Abstract:
Let I\subset K[x,y] be a -primary monomial ideal where K is a field. This paper produces an algorithm for computing the Ratliff-Rush closure I for the ideal I= whenever m_{i} is contained in the integral closure of the ideal . This generalizes of the work of Crispin \cite{Cri}. Also, it provides generalizations and answers for some questions given in \cite{HJLS}, and enables us to construct infinite families of Ratliff-Rush ideals.

Abstract:
Starting from \cite{Ayy2} we compute the Groebner basis for the defining ideal, P, of the monomial curves that correspond to arithmetic sequences, and then give an elegant description of the generators of powers of the initial ideal of P, inP. The first result of this paper introduces a procedure for generating infinite families of Ratliff-Rush ideals, in polynomial rings with multivariables, from a Ratliff-Rush ideal in polynomial rings with two variables. The second result is to prove that all powers of inP are Ratliff-Rush. The proof is through applying the first result of this paper combined with Corollary (12) in \cite{Ayy4}. This generalizes the work of \cite{Ayy1} (or \cite{Ayy11}) for the case of arithmetic sequences. Finally, we apply the main result of \cite{Ayy3} to give the necessary and sufficient conditions for the integral closedness of any power of inP.

Abstract:
Given the monomial ideal I=(x_1^{{\alpha}_1},...,x_{n}^{{\alpha}_{n}})\subset K[x_1,...,x_{n}] where {\alpha}_{i} are positive integers and K a field and let J be the integral closure of I . It is a challenging problem to translate the question of the normality of J into a question about the exponent set {\Gamma}(J) and the Newton polyhedron NP(J). A relaxed version of this problem is to give necessary or sufficient conditions on {\alpha}_1,...,{\alpha}_{n} for the normality of J. We show that if {\alpha}_{i}\epsilon{s,l} with s and l arbitrary positive integers, then J is normal.

Abstract:
In this article we produce Groebner bases for the defining ideal of a monomial curve that corresponds to an almost arithmetic sequence of positive integers, correcting previous work of Sengupta,(2003).

Abstract:
We prove that the initial ideal of the defining ideal of a monomial curve that corresponds to an almost arithmetic sequence of positive integers is Ratliff-Rush closed.

Abstract:
In this paper we study fundamental geometric properties of doubly warped product immersion which is an extension of warped product immersion. Moreover, we study geometric inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds.