Krawcewicz, Wieslaw
Permanent URI for this collectionhttps://hdl.handle.net/10735.1/2388
Dr. Wieslaw Krawcewicz became the head of the Department of Mathematical Sciences in 2009. He is an expert in topological equivariant nonlinear analysis, an interdisciplinary branch of math with applications in physics, chemistry, mathematical biology, engineering and medicine. Learn more about Prof. Krawcewicz on his home page and on Research Explorer
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Item Solutions of Fixed Period in the Nonlinear Wave Equation on Networks(Birkhauser Verlag AG, 2019-06-15) García-Azpeitia, C.; Krawcewicz, Wieslaw; Lv, Y.; Krawcewicz, WieslawThe wave equation on network is defined by ∂_{tt}u=Δ_{G}u+g(u), where u∊ℝⁿ and the graph Laplacian Δ_G is an operator on functions on n vertices. We suppose that g:ℝⁿ→ℝⁿ is an odd continuous function that satisfies g(0)=0, Dg(0)=0 and the Nagumo condition. Assuming that the graph is invariant by a subgroup of permutations Γ, using a Γ-equivariant topological invariant we prove the existence of multiple non-constant p-periodic solutions characterized by their symmetries.Item Altered Amygdala Connectivity in Individuals with Chronic Traumatic Brain Injury and Comorbid Depressive Symptoms(Frontiers Media S.A.) Han, Kihwan; Chapman, Sandra Bond; Krawczyk, Daniel C.; 0000 0003 5170 3614 (Chapman, SB); 0000-0002-4574-7306 (Han, K); Han, Kihwan; Chapman, Sandra Bond; Krawczyk, Daniel C.Depression is one of the most common psychiatric conditions in individuals with chronic traumatic brain injury (TBI). Though depression has detrimental effects in TBI and network dysfunction is a "hallmark" of TBI and depression, there have not been any prior investigations of connectivity-based neuroimaging biomarkers for comorbid depression in TBI. We utilized resting-state functional magnetic resonance imaging to identify altered amygdala connectivity in individuals with chronic TBI (8 years post injury on average) exhibiting comorbid depressive symptoms (N = 31), relative to chronic TBI individuals having minimal depressive symptoms (N = 23). Connectivity analysis of these participant sub-groups revealed that the TBI-plus-depressive symptoms group showed relative increases in amygdala connectivity primarily in the regions that are part of the salience, somatomotor, dorsal attention, and visual networks P(voxel) < 0.01, P(cluster) < 0.025). Relative increases in amygdala connectivity in the TBI-plus-depressive symptoms group were also observed within areas of the limbic cortical mood regulating circuit (the left dorsomedial and right dorsolateral prefrontal cortices and thalamus) and the brainstem. Further analysis revealed that spatially dissociable patterns of correlation between amygdala connectivity and symptom severity according to subtypes (Cognitive and Affective) of depressive symptoms (p(voxel) < 0.01, p(duster) < 0.025). Taken together, these results suggest that amygdala connectivity may be a potentially effective neuroimaging biomarker for comorbid depressive symptoms in chronic TBI.Item On Mathematical Contributions of Petr Petrovich Zabreiko(2012-09-05) Balanov, Zalman, 1959-; Gaishun, I.; Gorohovik, V.; Krawcewicz, Wieslaw; Lebedev, A.; 0000 0001 1616 0605 (Krawcewicz, W); 89645792 (Krawcewicz, W); Krawcewicz, WieslawNo abstract available.Item Stabilization in a State-Dependent Model of Turning Processes(SIAM, 2012-01-03) Hu, Qingwen; Krawcewicz, Wieslaw; Turi, Jànos; 0000 0001 1616 0605 (Krawcewicz, W); 0000 0000 4128 774X (Turi, J); 89645792 (Krawcewicz, W); 88656618 (Turi, J); Hu, Qingwen; Krawcewicz, Wieslaw; Turi, JànosWe consider a two-degree-of-freedom model for turning processes which involves a system of differential equations with state-dependent delay. Depending on process parameters (e.g., spindle speed, depth of cut) the cutting tool can exhibit unwanted vibrations, resulting in a nonsmooth surface of the workpiece. In this paper we propose a feedback law to stabilize the turning process for a large range of system parameters. The feedback law introduces a generic nonhyperbolic stationary point into the model, which generates the main technical challenge of this work. We establish the stability equivalence between the differential equations with state-dependent delay and a corresponding nonlinear system with the delay fixed at its stationary value. Then we show the stability of that nonlinear system with constant delay by computing its normal form. Finally, we obtain conditions on system parameters which guarantee the stability of the state-dependent delay model at the nonhyperbolic stationary point. ©2012 Society for Industrial and Applied Mathematics.Item Global Stability Lobes of Turning Processes with State-Dependent Delay(SIAM, 2012-09-13) Hu, Qingwen.; Krawcewicz, Wieslaw; Turi, Jànos; 0000 0001 1616 0605 (Krawcewicz, W); 0000 0000 4128 774X (Turi, J); 89645792 (Krawcewicz, W); 88656618 (Turi, J); Hu, Qingwen.; Krawcewicz, Wieslaw; Turi, JànosWe obtain global stability lobes of two models of turning processes with inherit nonsmoothness due to the presence of state-dependent delays. In the process, we transform the models with state-dependent delays into systems of differential equations with both discrete and distributed delays and develop a procedure to determine analytically the global stability regions with respect to parameters. We find that the spindle speed control strategy that we investigated in [SIAM J. Appl. Math., 72 (2012), pp. 1–24] can provide essential improvement on the stability of turning processes with state-dependent delay, and furthermore we show the existence of a proper subset of the stability region which is independent of system damping. Numerical simulations are presented to illustrate the general results..