Path-dependent Hamilton-Jacobi equations in infinite dimensions

We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and stability) for minimax solutions. A particular novelty is a suitable combination of minimax and viscosity solution techniques in the proof of the comparison principle. One of the main difficulties, the lack of compactness in infinite-dimensional Hilbert spaces, is circumvented by working with suitable compact subsets of our path space. As an application, our theory makes it possible to employ the dynamic programming approach to study optimal control problems for a fairly general class of (delay) evolution equations in the variational framework. Furthermore, differential games associated to such evolution equations can be investigated following the Krasovskii-Subbotin approach similarly as in finite dimensions.Comment: Final version, 53 pages, to appear in Journal of Functional Analysi

Psoriasiform Sarcoidosis Presenting in Pregnancy and Treatment Considerations

Cutaneous sarcoidosis is a common presentation for patients with sarcoidosis. Rarely, patients can present with psoriasiform lesions mimicking chronic plaque psoriasis. Here, we present a case of psoriasiform sarcoidosis in a pregnant patient. Pregnancy represents a unique challenge to systemic treatments if topical management fails. Tumor necrosis factor alpha inhibitors warrant special consideration during pregnancy

Cold Harbor to the Crater: The End of the Overland Campaign

Fresh Perspectives on an Overlooked Portion of the Overland Campaign At long last UNC Press’s vaunted Military Campaigns of the Civil War series has returned under the careful co-editorship of Gary Gallagher and Caroline Janney. A well-written, well-researched, and topically comprehensive...

Constraint Quantization of Slave-Particle Theories

We start from the Barnes-Coleman slave-particle description, where the Hubbard operators $X$ are decomposed into a product of fermionic ($f_{\alpha}$) and bosonic ($b$) operators. The quantum mechanical constraint $b^{\dagger} b + \sum_{\alpha} f_{\alpha}^{\dagger} f_{\alpha} = 1$ is treated within the framework of Dirac's method for the quantization of classical constrained systems. This leads to modified algebraic properties of the fundamental operators: $b b^{\dagger} b = b$, $f_{\alpha} f_{\beta}^{\dagger} f_{\gamma} = \delta_{\alpha \beta} f_{\gamma}$ and $f_{\alpha} b^{\dagger}= 0$. Thereby the algebra of the $X$-operators is preserved exactly on the operator level. Matrix representations of the above algebra are constructed and a resolvent-like perturbation theory for the single-impurity Anderson model is developed.Comment: LATEX, 5 page

Leonidas Polk: Warrior Bishop of the Confederacy

General Leonidas Polk has become one of the “whipping boys” over the years for many of the failures of the Confederacy’s Army of Tennessee in the Western Theater. His name alone conjures up inside jokes among seasoned military historians of the Civil War, and all too often this important leader is depicted in serious analyses of the Western campaigns as an incompetent fool. When portrayed alongside the fractious Braxton Bragg, under whom he served and with whom he engaged in bitter quarrels, and juxtaposed against Federal luminaries U.S. Grant and William T. Sherman, Polk generally receives poor marks as a commander. Some of those criticisms, flung by scholars who have studied the Western Theater in depth, such as T. Harry Williams, Thomas Connelly, Grady McWhiney, Steven Woodworth, and Peter Cozzens, are well-deserved. Others, as Huston Horn successfully proves in his new biography of the general, are not, or should be reconsidered in light of the historical context. Hopefully, after perusing this impressive book, many readers will agree with him

Petersburg to Appomattox: The End of the War in Virginia

In this latest installment of UNC Press’s Military Campaigns of the Civil War series, Caroline E. Janney has made a strong mark for herself as Gary W. Gallagher’s literary successor. Most readers will be familiar with the storied list of previous titles in the series, the last of which on the end of the Overland Campaign and the Siege of Petersburg saw Janney and Gallagher team up as co-editors. That was a fine volume. This one is possibly even better. One big reason this book succeeds is the uniform quality of writing among the nine essays, which range from traditional military analyses of Grant’s and Sheridan’s roles to more socio-cultural topics, such as how African-Americans reacted to Lee’s surrender. It is a true mix of sub-niches within the subfield of Civil War history, but the variety of historians and essays—a hallmark of Gallagher’s previously edited works—provides a satisfyingly rich texture without going overboard on “drums and trumpets” or losing oneself in the weeds of micro-history. As one currently editing his own anthology, I can certainly attest to the difficulty of striking the happy balance