Equivalence of inverse Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter

Three inverse problems for a Sturm-Liouville boundary value problem −y″+qy=λy, y(0)cosα=y′(0)sinα and y′(1)=f(λ)y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.     

Simultaneous separation and determination (in serum) of phenytoin and carbamazepine and their deuterated analogues by high-performance liquid chromatography--ultraviolet detection for tracer studies

The use of stable isotope-labeled tracer compounds is the safest and most effective method to perform many steady state pharmacokinetic and drug interaction studies. We describe a method by which the heavily deuterated 2H10 analogues of carbamazepine (2H10 CBZ) and phenytoin (2H10 PHT) can be chromatographically separated by high-performance liquid chromatography from unlabeled CBZ and PHT. All compounds are quantitated against an internal standard (IS) (10,11-dihydrocarbamazepine) and measured using conventional UV detection rather than mass spectrometry. Baseline resolution of extracted serum containing 2H10 CBZ, CBZ, 2H10 PHT, PHT and IS is achieved on a heated (55 degrees C) 25 cm x 4.6 mm BioAnalytical Systems Phase II 5 microns ODS column with an isocratic mobile phase consisting of water-acetonitrile-tetrahydrofuran (80:16:4, v/v/v) at 1.2 ml/min. Eluting compounds were monitored at a UV wavelength of 214 nm. Calculated resolution of 2H10 CBZ from CBZ and of 2H10 PHT from PHT were 1.3. Serum standard curves were linear (R greater than or equal to 0.999) over a range of 0.5-14 micrograms/ml for 2H10 CBZ, 0.5-20 micrograms/ml for CBZ, 0.5-20 micrograms/ml for 2H10 PHT, and 0.5-30 micrograms/ml for PHT. Within-day percent relative standard deviations (precision) were less than 6% in all cases.     

Simultaneous determination of p-hydroxylated and dihydrodiol metabolites of phenytoin in urine by high-performance liquid chromatography

Accurate urinary measurements of the two major metabolites of phenytoin, 5-(p-hydroxyphenyl)-5-phenylhydantoin (p-HPPH) and 5-(3,4-dihydroxy-cyclohexa-1,5-dienyl)-5-phenylhydantoin (dihydrodiol, DHD), are necessary for pharmacokinetic and drug-interaction studies of this commonly used antiepileptic drug. We describe a simple, rapid, acid hydrolysis, with liquid-liquid extraction and simultaneous isocratic reversed-phase high-performance liquid chromatography of p-HPPH and 5-(m-hydroxyphenyl)-5-phenylhydantoin (m-HPPH) (hydrolytic end product of DHD). p-HPPH and m-HPPH were quantitated against their separate respective internal standards of alphenal and tolylbarb. The mobile phase consisted of water-dioxane-tetrahydrofuran (80:15:5, v/v/v) at 2 ml/min and at 50 degrees C, with detection at 225 nm. Baseline separation was achieved by use of a 16 cm x 3.9 mm Nova-Pak C18 column and total analysis time of 12 min. p-HPPH and m-HPPH concentrations ranged from 10 to 200 and from 2 to 30 micrograms/ml, respectively, with between-day coefficients of variations of 3.3-4.5% and 2.2-5.1% for controls. All standard curves were linear with r values greater than 0.993. The DHD concentration was determined by multiplying m-HPPH concentrations by 2.3.     

A completeness theorem for a nonlinear multiparameter eigenvalue problem

In this paper we study the linked nonlinear multiparameter system

$\text{y}{}_{\mathrm{r}}{}^{\mathrm{n}}\text{(X}{}_{\mathrm{r}}\text{) + M}{}_{\mathrm{r}}\text{Y}{}_{\mathrm{r}}\text{+}\text{∑}\text{s=1}\text{k}\text{λ}{}_{\mathrm{s}}\text{(a}{}_{\mathrm{rs}}\text{(X}{}_{\mathrm{r}}\text{) + P}{}_{\mathrm{rs}}\text{) Y}{}_{\mathrm{r}}\text{(X}{}_{\mathrm{r}}\text{) = 0, r = l,…, k}$

, where x_r? [a_r, b_r], y_r is subject to Sturm-Liouville boundary conditions, and the continuous functions a_rs satisfy ¦ $\text{A ¦ (x) =}\text{det}\text{a}{}_{\mathrm{rs}}\text{(x}{}_{\mathrm{r}}\text{) > 0}$. Conditions on the polynomial operators M_r, P_rs are produced which guarantee a sequence of eigenfunctions for this problem yⁿ(x) = Π_r=1^ky_rⁿ(x_r), n ? 1, which form a basis in $\text{L}{}^2\text{([a, b], ¦ A ¦)}$. Here [a, b] = [a₁, b₁ × … × [a_k, b_k].     

Isolation of teratogenic alkaloids by reversed-phase high-performance liquid chromatography

Reversed-phase high-performance liquid chromatography was used for both analytical and preparative separations of several steroidal alkaloids which occur in extracts of Veratrum californicum. The inclusion of 0.1% trifluoroacetic acid in the mobile phase improved the efficiency of the chromatography and the solubility of the compounds in aqueous acetonitrile. Nuclear magnetic resonance was used to assist the identification of the isolated steroidal alkaloids. The effect of the interaction of trifluoroacetic acid with the alkaloids could be clearly seen by changes in the chemical shifts in the nuclear magnetic resonance spectra.     

Stronger quantum correlations with loophole-free postselection

One of the most striking nonclassical features of quantum mechanics is in the correlations it predicts between spatially separated measurements. In local hidden variable theories, correlations are constrained by Bell inequalities, but quantum correlations violate these. However, experimental imperfections lead to loopholes whereby LHV correlations are no longer constrained by Bell inequalities, and violations can be described by LHV theories. For example, loopholes can emerge through selective detection of events. In this Letter, we introduce a clean, operational picture of multiparty Bell tests, and show that there exists a nontrivial form of loophole-free postselection. Surprisingly, the same postselection can enhance quantum correlations, and unlock a connection between nonclassical correlations and nonclassical computation.