Congenital lateral dislocation of the patella is a rare condition caused by displacement of the extensor mechanism of the knee, which occurs before or shortly after birth (Malkin 1932). The patella is small and cannot be replaced in its normal position except by operation. This type of dislocation differs from recurrent or habitual dislocation of the patella, which occurs during childhood or ad...

B. M. Ellingson, D. P. Bedekar, M. G. Malkin, S. D. Rand, A. Hoyt, J. Connelly, S. N. Kurpad, and K. M. Schmainda Translational Brain Tumor Program, Medical College of Wisconsin, Milwaukee, WI, United States, Department of Radiology, Medical College of Wisconsin, Milwaukee, WI, United States, Department of Neurology, Medical College of Wisconsin, Milwaukee, WI, United States, Department of Neur...

We consider a system of differential equations possessing a family of T -periodic solutions and subjected to a T -periodic Lipschitz small perturbation. We prove the existence and uniqueness of a T -periodic solution of the perturbed system by means of a Lipschitz generalization of the Lyapunov–Schmidt reduction method. When the perturbation is continuously differentiable our result coincides w...

P. S. LaViolette, B. M. Ellingson, J. M. Connelly, M. G. Malkin, S. D. Rand, and K. M. Schmainda Biophysics, Medical College of Wisconsin, Milwaukee, WI, United States, Translational Brain Tumor Program, Medical College of Wisconsin, Milwaukee, WI, United States, Radiology, Medical College of Wisconsin, Milwaukee, WI, United States, Neurology, Medical College of Wisconsin, Milwaukee, WI, United...

In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase den...

JESSE D. MALKIN, M.Phil., Ph.D., worked on this paper while at Covance Health Economics and Outcomes Services Inc., Gaithersburg, Maryland. He is currently with the RAND Corporation, Arlington, Virginia; STACEY J. ACKERMAN, MSE, Ph.D., is with Covance Health Economics and Outcomes Services Inc.; JEFF SCHEIN, Dr.Ph, M.Ph., and JULIE LOCKLEAR, Pharm.D., are with Janssen Pharmaceutica, Titusville,...

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including ordinary Hamiltonian G-spaces, Lu’s momentum maps of Poisson group actions, and the group-valued momentum maps of Alekseev–Malkin–Meinrenken. More precisely, we carry out the following program: (1) We de...

Definition 1 (Search problem). In SearchLWE[n, α, q], the goal is, given oracle access to LWEs for some fixed s ∼ UZnq , to find and output s. Definition 2 (Decision problem). In DecisionLWE[n, α, q], given oracle access to some oracle O along with the promise that it either outputs samples (a) from LWEs (for some fixed s ∼ UZnq ) or (b) drawn uniformly at random in Zq ×Zq, the goal is to decid...

For prediction of polymer systems behavior on processing and exploiting stages knowledge of phase diagrams is very useful and in some cases – necessary. They characterize equilibrium phase states and for particular systems – phase structure. Among other methods to estimate compatibility of two substances including polymeric one, and consequently to obtain reasonable information about phase stat...