Hyperpolarized 13C Magnetic Resonance Imaging of Fumarate Metabolism by Parahydrogen-induced Polarization: A Proof-of-Concept in vivo Study

Hyperpolarized [1-¹³C]fumarate is a promising magnetic resonance imaging (MRI) biomarker for cellular necrosis, which plays an important role in various disease and cancerous pathological processes. To demonstrate the feasibility of MRI of [1-¹³C]fumarate metabolism using parahydrogen-induced polarization (PHIP), a low-cost alternative to dissolution dynamic nuclear polarization (dDNP), a cost-effective and high-yield synthetic pathway of hydrogenation precursor [1-¹³C]acetylenedicarboxylate (ADC) was developed. The trans-selectivity of the hydrogenation reaction of ADC using a ruthenium-based catalyst was elucidated employing density functional theory (DFT) simulations. A simple PHIP set-up was used to generate hyperpolarized [1-¹³C]fumarate at sufficient ¹³C polarization for ex vivo detection of hyperpolarized ¹³C malate metabolized from fumarate in murine liver tissue homogenates, and in vivo ¹³C MR spectroscopy and imaging in a murine model of acetaminophen-induced hepatitis.     

Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point,II — Its relevance to the Mathieu equation and the Legendre equation

We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.     

Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Let be a surjective mapping from a uniform algebra on a compact Hausdorff space onto a uniform algebra on a compact Hausdorff space . Suppose that holds for every . Then we have that is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).

     

Classification of extremal contractions from smooth fourfolds of -type

We investigate divisorial contractions of extremal rays from
smooth fourfolds. When the exceptional divisor is contracted to a curve, we prove that the divisor is a -bundle or quadric bundle over a smooth curve and the contraction is the blowing up along the curve. Furthermore we determine the local analytic structure of the contraction.

     

Global stability of a generalized epidemic model

The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable — the global result has not been established previously.     

Discreteness and rationality of F-jumping numbers on singular varieties

We prove that the F-jumping numbers of the test ideal t(X; D, \mathfraka^t){\tau(X; \Delta, \mathfrak{a}^t)} are discrete and rational under the assumptions that X is a normal and F-finite scheme over a field of positive characteristic p, K _X  + Δ is \mathbb Q{\mathbb {Q}}-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals \mathfraka{\mathfrak{a}} is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero.     

Generalizations of spectrally multiplicative surjections between uniform algebras

Let $ A $ A and ℬ be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: $ A $ A → ℬ with S(1)=T(1)= 1 and α ∈ ℂ \ {0} satisfy r(S(a)T(b) − α)= r(ab− α) for all a,b ∈ $ A $ A , then S=T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σ _π (S(p)T(q)) ⊂ σ _π (ρ(p) τ(q)) for all p,q ∈ I, where σ _π (f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions “enough”. There exists a homeomorphism ϕ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(ϕ(y)) and T(p)(y)= τ(p)(ϕ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A.     

When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.