Factorization of Q(h(T)(x)) over a finite field,where Q(x) is irreducible and h(T)(x) is linear II

Let GF(q) be the finite field of order q, let Q(x) be an irreducible polynomial in GF(qⁱ)[x], and let H(x) = h(T)(x) be a linear polynomial in GF(q)[x]. We give the degrees of the irreducible factors of Q(H(x)) in GF(qⁱ)[x], and the number of irreducible factors of each degree. We consider the special cases when H(x) is a trace function, and when h(x) is cyclotomic. Finally, we give several examples.     

Ab initio and analytic intermolecular potentials for Ar-CH(3)OH

Ab initio calculations at the CCSD(T)/aug-cc-pVTZ level of theory were used to characterize the Ar-CH(3)OH intermolecular potential energy surface (PES). Potential energy curves were calculated for four different Ar + CH(3)OH orientations and used to derive an analytic function for the intermolecular PES. A sum of Ar-C, Ar-O, Ar-H(C), and Ar-H(O) two-body potentials gives an excellent fit to these potential energy curves up to 100 kcal mol(-1), and adding an additional r(-n) term to the Buckingham two-body potential results in only a minor improvement in the fit. Three Ar-CH(3)OH van der Waals minima were found from the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculations. The structure of the global minimum is in overall good agreement with experiment (X.-C. Tan, L. Sun and R. L. Kuczkowski, J. Mol. Spectrosc., 1995, 171, 248). It is T-shaped with the hydroxyl H-atom syn with respect to Ar. Extrapolated to the complete basis set (CBS) limit, the global minimum has a well depth of 0.72 kcal mol(-1) with basis set superposition error (BSSE) correction. The aug-cc-pVTZ basis set gives a well depth only 0.10 kcal mol(-1) smaller than this value. The well depths of the other two minima are within 0.16 kcal mol(-1) of the global minimum. The analytic Ar-CH(3)OH intermolecular potential also identifies these three minima as the only van der Waals minima and the structures predicted by the analytic potential are similar to the ab initio structures. The analytic potential identifies the same global minimum and the predicted well depths for the minima are within 0.05 kcal mol(-1) of the ab initio values. Combining this Ar-CH(3)OH intermolecular potential with a potential for a OH-terminated alkylthiolate self-assembled monolayer surface (i.e., HO-SAM) provides a potential to model Ar + HO-SAM collisions.     

Hofer geometry of a subset of a symplectic manifold

To every closed subset X of a symplectic manifold (M, ω) we associate a natural group of Hamiltonian diffeomorphisms Ham (X, ω). We equip this group with a semi-norm ${\Vert\cdot\Vert^{X, \omega}}$ , generalizing the Hofer norm. We discuss Ham (X, ω) and ${\Vert\cdot\Vert^{X, \omega}}$ if X is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of X in M. Its first part states that for the unit sphere in ${\mathbb{R}^{2n}}$ this diameter is bounded below by ${\frac{\pi}{2}}$ , if n ≥ 2. Its second part states that for n ≥ 2 and d ≥ n there exists a compact subset X of the closed unit ball in ${\mathbb{R}^{2n}}$ , such that X has Hausdorff dimension at most d + 1 and relative Hofer diameter bounded below by π / k(n, d), where k(n, d) is an explicitly defined integer.     

A Novel Prospective Study Assessing the Combination of Photodynamic Therapy and Proton Radiation Therapy: Safety and Outcomes When Treating Malignant Pleural Mesothelioma

Malignant pleural mesothelioma remains difficult to treat, with high failure rates despite optimal therapy. We present a novel prospective trial combining proton therapy (PT) and photodynamic therapy (PDT) and the largest‐ever mesothelioma PT experience (n = 10). PDT photosensitizers included porfimer sodium (2 mg·kg^?1; 24 h drug‐light interval) or 2‐[1‐hexyloxyethyl]‐2‐devinyl pyropheophorbide‐a (HPPH) (4 mg·m^?2;48 h) with wavelengths of 630 nm to 60J·cm^?2 and 665 nm to 15‐45J·cm^?2, respectively. With a median age of 69 years, patients were predominantly male (90%) with epithelioid histology (100%) and stage III‐IV disease (100%). PT was delivered to a median of 55.0 CGE/1.8‐2.0 CGE (range 50–75 CGE) adjuvantly (n = 8) or as salvage therapy (n = 2) following extended pleurectomy/decortication (ePD)/PDT. Two‐year local control was 90%, with distant and regional failure rates of 50% and 30%, respectively. All patients received chemotherapy, and four received immunotherapy. Surgical complications included atrial fibrillation (n = 3), pneumonia (n = 2), and deep vein thrombosis (n = 2). Median survival from PT completion was 19.5 months (30.3 months from diagnosis), and 1‐ and 2‐year survival rates were 58% and 29%. No patient experienced CTCAEv4 grade ≥2 acute or late toxicity. Our prolonged survival in very advanced‐stage patients compares favorably to survival for PT without PDT and photon therapy with PDT, suggesting possible spatial or systemic cooperativity and immune effect.     

Chemical Derivatization and Characterization of Novel Antitrypanosomals for African Trypanosomiasis

The search for novel antitrypanosomals and the investigation into their mode of action remain crucial due to the toxicity and resistance of commercially available antitrypanosomal drugs. In this study, two novel antitrypanosomals, tortodofuordioxamide (compound 2) and tortodofuorpyramide (compound 3), were chemically derived from the natural N-alkylamide tortozanthoxylamide (compound 1) through structural modification. The chemical structures of these compounds were confirmed through spectrometric and spectroscopic analysis, and their in vitro efficacy and possible mechanisms of action were, subsequently, investigated in Trypanosoma brucei (T. brucei), one of the causative species of African trypanosomiasis (AT). The novel compounds 2 and 3 displayed significant antitrypanosomal potencies in terms of half-maximal effective concentrations (EC₅₀) and selectivity indices (SI) (compound 1, EC₅₀ = 7.3 μM, SI = 29.5; compound 2, EC₅₀ = 3.2 μM, SI = 91.3; compound 3, EC₅₀ = 4.5 μM, SI = 69.9). Microscopic analysis indicated that at the EC₅₀ values, the compounds resulted in the coiling and clumping of parasite subpopulations without significantly affecting the normal ratio of nuclei to kinetoplasts. In contrast to the animal antitrypanosomal drug diminazene, compounds 1, 2 and 3 exhibited antioxidant absorbance properties comparable to the standard antioxidant Trolox (Trolox, 0.11 A; diminazene, 0.50 A; compound 1, 0.10 A; compound 2, 0.09 A; compound 3, 0.11 A). The analysis of growth kinetics suggested that the compounds exhibited a relatively gradual but consistent growth inhibition of T. brucei at different concentrations. The results suggest that further pharmacological optimization of compounds 2 and 3 may facilitate their development into novel AT chemotherapy.