Rm SO Research Articles

Local rigidity of hyperbolic 3-manifolds after Dehn surgery

It is well known that some lattices in ${\rm SO}(n,1)$ can be nontrivially deformed when included in ${\rm SO}(n+1,1)$ (e.g., via bending on a totally geodesic hypersurface); this contrasts with the (super) rigidity of higher rank lattices. M. Kapovich recently gave the first examples of lattices in ${\rm SO}(3,1)$ which are locally rigid in ${\rm SO}(4,1)$ by considering closed hyperbolic $3$-manifolds obtained by Dehn filling on hyperbolic two-bridge knots. We generalize this result to Dehn filling on a more general class of one-cusped finite volume hyperbolic $3$-manifolds, allowing us to produce the first examples of closed hyperbolic $3$-manifolds which contain embedded quasi-Fuchsian surfaces but are locally rigid in ${\rm SO}(4,1)$.

The highest lowest zero and other applications of positivity

The first nontrivial zeros of the Riemann $zeta$-function are $\approx1/2\pm 14:13472i$. We investigate the question of whether or not any other $L$-function has a higher lowest zero. To do so, we try to quantify the notion that the $L$-function of a "small" automorphic representation (i.e., one with small level and archimedean type) does not have small zeros, and vice-versa. We prove that many types of automorphic $L$-functions have a lower first zero than $\zetas$'s (see Theorems 1.1 and 1.2). This is done using Weil's explicit formula with carefully chosen test functions. When this method does not immediately show that $L$-functions of a certain type have low zeros, we then attempt to turn the tables and show that no $L$-functions of that type exist. Thus, the argument is a combination of proving that low zeros exist and that certain cusp forms do not. Consequently, we are able to prove vanishing theorems and improve upon existing bounds on the Laplace spectrum on $L\sp 2({\rm SL}\sb n(\mathbb {Z})\backslash{\rm SL}\sb n(\mathbb {R})/{\rm SO}\sb n(\mathbb {R}))$. These in turn can be used to show that ${\rm SL}\sb 68(\mathbb {Z})\backslash{\rm SL}\sb 68(\mathbb {R})/{\rm SO}\sb 68(\mathbb {R})$ has a discrete, nonconstant, noncuspidal eigenvalue outside the range of the continuous spectrum on $L\sp 2({\rm SL}\sb 68(\mathbb {R})/{\rm SO}\sb 68(\mathbb {R}))$, but that this never happens for ${\rm SL}\sb n(\mathbb {Z})\backslash/{\rm SL}\sb n(\mathbb {R})/{\rm SO}\sb n(\mathbb {R})$ in lower rank. Another application is to cuspidal cohomology: we show there are no cuspidal harmonic forms on ${\rm SL}\sb n(\mathbb {Z})\backslash{\rm SL}\sb n(\mathbb {R})/{\rm SO}\sb n(\mathbb {R})$ for $n<27$.

Simultaneous and Fast Detection of Anions in Snow Using Short Tube by Capillary Zone Electrophoresis

A capillary zone electrophoresis (CZE) method applied short-effective length of capillary (11 cm) and low separation voltage (5 kV) was developed for the fast and quantitative determination of Cl m , $ {\\rm NO}_2^ - $ , $ {\\rm SO}_4^{2 - } $ , $ {\\rm NO}_3^ - $ , $ {\\rm HCO}_3^ - $ in snow sample. Baseline separation of inorganic anions and organic anions was achieved within 55 s. Indirect absorbance detection of anions was accomplished with a chromate - based background electrolyte modified with cetyltrimethylammonium bromide (CTAB) and acetonitrile at pH 9.5. The effect of the pH, the concentration of electrolyte and modifiers on the resolution was investigated. The application of electrokinetic injection using butyric acid as internal standard created the described method fast, sensitive, and quantitative, with good relative standard deviation (RSD), for migration times from 0.1 to 0.3% and for peak areas from 1.8 to 4.0%. The limits of detection (LOD) were 0.03 mg L m 1 Cl m , 0.1 mg L m 1 $ {\\rm NO}_2^ - $ , 0.07 mg L m 1 $ {\\rm SO}_4^{2 - } $ , 0.08 mg L m 1 $ {\\rm NO}_3^ - $ , 0.05 mg L m 1 F m , and 0.2 mg L m 1 $ {\\rm HCO}_3^ - $ , respectively. Standard addition recoveries of Cl m , $ {\\rm NO}_2^ - $ , $ {\\rm SO}_4^{2 - } $ , $ {\\rm NO}_3^ - $ , F m , and $ {\\rm HCO}_3^ - $ in snow sample were between 91 and 104%. This method has been shown promising results for the determination of small anions in snow sample.

A Spectral Line Survey from 138.3 to 150.7 GHz toward Orion‐KL

We present the results of a spectral line survey from 138.3 to 150.7 GHz toward Orion-KL. The observations were made using the 14 m radio telescope of Taeduk Radio Astronomy Observatory. Typical system temperatures were between 500 and 700 K, with the sensitivity between $0.02 - 0.06$ K in units of $\rm T_A^*$. A total of 149 line spectra are detected in this survey. Fifty lines have been previously reported, however we find 99 new detections. Among these new lines, 32 are `unidentified', while 67 are from molecular transitions with known identifications. There is no detection of H or He recombination lines. The identified spectra are from a total of 16 molecular species and their isotopic variants. In the range from 138.3 to 150.7 GHz, the strongest spectral line is the J=3-2 transition of CS molecule, followed by transitions of the $\rm H_2CO$, $\rm CH_3OH$, $\rm CH_3CN$, and $\rm SO_2$. Spectral lines from the large organic molecules such as $\rm CH_3OH$, $\rm CH_3OCH_3$, $\rm HCOOCH_3$, $\rm C_2H_5CN$ and $\rm CH_3CN$ are prominent; with 80 % of the identified lines arising from transitions of these molecules. The rotational temperatures and column densities are derived using the standard rotation diagram analysis for $\rm CH_3OH$ ($\rm ^{13}CH_3OH$), $\rm HCOOCH_3$, $\rm CH_3CN$ and $\rm SO_2$ with $\rm 10\sim 270 K$ and $\rm 0.2\sim 20\times 10^{15} cm^{-2}$. These estimates are fairly comparable to the values for the same molecule in other frequency regions by other studies.

The closure ordering of adjoint nilpotent orbits in $\mathfrak{so}(p,q)$

Let ${\mathcal O}$ be a nilpotent orbit in $\mathfrak{so}(p,q)$ under the adjoint action of the full orthogonal group ${\rm O}(p,q)$. Then the closure of ${\mathcal O}$ (with respect to the Euclidean topology) is a union of ${\mathcal O}$ and some nilpotent ${\rm O}(p,q)$-orbits of smaller dimensions. In an earlier work, the first author has determined which nilpotent ${\rm O}(p,q)$-orbits belong to this closure. The same problem for the action of the identity component ${\rm SO}(p,q)^0$ of ${\rm O}(p,q)$ on $\mathfrak{so}(p,q)$ is much harder and we propose a conjecture describing the closures of the nilpotent ${\rm SO}(p,q)^0$-orbits. The conjecture is proved when $\min(p,q)\le7$. Our method is indirect because we use the Kostant-Sekiguchi correspondence to translate the problem to that of describing the closures of the unstable orbits for the action of the complex group ${\rm SO}_p({\bf C})\times{\rm SO}_q({\bf C})$ on the space $M_{p,q}$ of complex $p\times q$ matrices with the action given by $(a,b)\cdot x=axb^{-1}$. The fact that the Kostant--Sekiguchi correspondence preserves the closure relation has been proved recently by Barbasch and Sepanski.

The two-well problem in three dimensions

We study properties of generalized convex hulls of the set \(K={\rm SO}3\cup{\rm SO}3 H\) with \({\rm det}\, H>0\). If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be nontrivial if H is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point then the polyconvex hull is trivial provided that there are no rank-1 connections.

On the ergodic properties of Cartan flows in ergodic actions of ${\bf SL}_{\bf 2}{\bf (R)}$ and ${\bf SO}{\bf ({\bi n},1)}$

Let $G={\rm SL_2({\bf R})}$ (or $G={\rm SO}(n,1)$) act ergodically on a probability space $(X,m)$. We consider the ergodic properties of the flow $(X,m,\{g_t\})$, where $\{g_t\}$ is a Cartan subgroup of $G$. The geodesic flow on a compact Riemann surface is an example of such a flow; here $X=G/\Gamma$ is a transitive $G$-space, $G={\rm SL_2({\bf R})}$ and $\Gamma\subset G$ is a lattice. In this case the flow is Bernoullian.For the general ergodic $G$-action, the flow $(X,m,\{g_t\})$ is always a $K$-flow, however there are examples in which it is not Bernoullian.

Exceptional Θ-Correspondences I

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. Let $G$ be either a split ${\rm SO}(2n+2)$, or a split adjoint group of type $E_n, (n=6,7,8)$, over a $p$-adic field. In this article we study correspondences arising by restricting the minimal representation of $G$ to various dual pairs in $G$.

Inflation at low scales: General analysis and a detailed model.

Models of inflationary cosmology based on spontaneous symmetry breaking typically suffer from the shortcoming that the symmetry breaking scale is driven to nearly the Planck scale by observational constraints. In this paper we investigate inflationary potentials in a general context, and show that this difficulty is characteristic only of potentials $V(\phi)$ dominated near their maxima by terms of order $\phi^2$. We find that potentials dominated by terms of order $\phi^m$ with \hbox{$m > 2$} can satisfy observational constraints at an arbitrary symmetry breaking scale. Of particular interest, the spectral index of density fluctuations is shown to depend only on the order of the lowest non-vanishing derivative of $V(\phi)$ near the maximum. This result is illustrated in the context of a specific model, with a broken ${\rm SO(3)}$ symmetry, in which the potential is generated by gauge boson loops.

On a multiplicity formula of weights of representations of ${\rm SO}\sp *(2n)$ and reciprocity theorems for symplectic groups

A formula relating the multiplicity of a weight of a holomorphic discrete series of the group $S{O^ \ast }(2n)$ to the frequency of occurrence of an irreducible holomorphically induced representation of the group $Sp(2n,\mathbb {C})$ in an

Minimal hypersurfaces of ${\bf R}\sp {2m}$ invariant by ${\rm SO}(m)\times {\rm SO}(m)$

Minimal hypersurfaces of ${\bf R}\sp {2m}$ invariant by ${\rm SO}(m)\times {\rm SO}(m)$

Thermal decomposition of potassium persulfate in aqueous solution at 50°C in the presence of ethyl acrylate

Potassium persulfate modes of thermal decomposition and reactions with ethyl acrylate in aqueous solution at 50°C in nitrogen atmosphere have been investigated. It has been found that the rate of persulfate decomposition may be expressed as −d(S2O)/dt ∝ (S2O)1.00 ± 0.06 × (M)0.92±0.05 while the steady state rate of polymerization (Rp) is given by Rp ∝ (S2O)0.50 ± 0.50 × (M)1.00 ± 0.06 in the concentration ranges of the persulfate, 10−3−10−2 (m/L), and monomer (M), 4.62−23.10 × 10−2 (m/L), i.e., within its solubility range. In the absence of monomer, the rate of persulfate decomposition was slow and first order in persulfate at the early stages of the reaction when the pH of the solution was above 3.0. The separating polymer phase was a stable colloid at low electrolyte concentrations even in the absence of micelle generators. It has been shown that the oxidation of water soluble monomeric and oligomeric radicals by the S2O ions in the aqueous phase, viz., \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm M}_j^ \cdot + {\rm S}_2 {\rm O}_8^{2 - } \to {\rm M}_j - {\rm O} - {\rm SO}_3^ - + {\rm SO}_4^{ \cdot - } $\end{document} is not kinetically significant in this system. It has been found that the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm M} + {\rm S}_2 {\rm O}_8^{2 - } \rightarrow{k}{\rm M} - {\rm O} - {\rm SO}_3^ - + {\rm SO}_4^{ \cdot - } $\end{document} would also lead to chain initiation at the outset of the polymerization reaction. k has been estimated as 5.41 × 10−5 (L/m/s) at 50°C. Taking kp as 103 (L/m/s), kt has been estimated as 0.168 × 106 (L/m/s). The partition confficient (β) of the monomer between the polymer phase and the aqueous phase was found to be 16 ± 2, at 50°C. The rate constant for persulfate ion dissociation has been found as 1.40 × 10−6 s−1 at 50°C.

Representations with cohomology in the discrete spectrum of subgroups of ${\rm SO}(n,1)({Z})$ and Lefschetz numbers

Representations with cohomology in the discrete spectrum of subgroups of ${\rm SO}(n,1)({Z})$ and Lefschetz numbers

The connection between the symmetric space $E_7/{\rm SO}(12)\cdot {\rm SO}(3)$ and projective planes

The connection between the symmetric space $E_7/{\rm SO}(12)\cdot {\rm SO}(3)$ and projective planes

The connection between the symmetric space $E_{(6)}/{\rm SO}(10)\cdot{\rm SO}(2)$ and projective planes

The connection between the symmetric space $E_{(6)}/{\rm SO}(10)\cdot{\rm SO}(2)$ and projective planes

${\rm SO}(3)$-connections and the topology of 4-manifolds

${\rm SO}(3)$-connections and the topology of 4-manifolds

Free Radical Mechanisms for the Oxidation of Substituted Ascorbates. A Pulse Radiolysis Study of L-Ascorbic Acid-2-Sulfate

The oxidations of L-ascorbate 2-sulfate by ${\rm Br}_{2}^{-}$ and OH radicals generated in aqueous solutions (pH 4.5-9.5) were studied by pulse radiolysis. The $(2\text{-}{\rm SO}_{4}{\rm A})\overline{\cdot}$ radical, generated in an electron transfer reaction between ${\rm Br}_{2}^{-}$ and the parent compound, loses sulfate (τ ∼ 500 μsec) to give ascorbate free radical $({\rm A}\overline{\cdot})$ with a $G({\rm A}\overline{\cdot})=2.0$. The oxidation of L-ascorbate 2-sulfate by OH radicals is complex, yielding both $(2\text{-}{\rm SO}_{4}{\rm A})\overline{\cdot}$ and OH radical adducts. Some of these transients subsequently yield ${\rm A}\overline{\cdot}$. HPLC studies corroborate the overall mechanism postulated for the oxidation of L-ascorbate 2-sulfate by OH radicals.

Classification of ${\rm SO}(3)$-actions on five-manifolds with singular orbits.

Classification of ${\rm SO}(3)$-actions on five-manifolds with singular orbits.

Studies of Spin-Trapped Radicals in γ-Irradiated Aqueous Solutions of Thymidine-5′-Monophosphate and Cytidine-5′-Monophosphate by Liquid Chromatography and ESR Spectroscopy

Aqueous solutions of thymidine-5′-monophosphate and cytidine-5′-monophosphate were γ-irradiated with 2-methyl-2-nitrosopropane as a spin-trapping reagent. Liquid chromatography was applied to separate the stable spin-trapped radicals in the irradiated solutions. The eluate was passed through flow cells of ESR and uv detectors and collected by a fraction collector. The amount of residual sugar in the each fraction was determined by the $\text{phenol-}{\rm H}_{2}{\rm SO}_{4}$ method. From the combined results of the ESR, uv, and sugar determinations, the structures of most of the trapped radicals were identified. The short-lived radicals which were trapped by 2-methyl-2-nitrosopropane were radicals on N-1, C-5, and N-3 positions of the base in the thymidine-5′-monophosphate and C-5 and C-6 base radicals in the cytidine-5′-monophosphate.

Quenching rate constants for the removal of SO2(3B1) by various fluorinated olefins

AbstractA competitive technique employing the SO2(3B1) photosensitized isomerization of cis‐C2F2H2 to trans‐C2F2H2 in the presence of selected fluorinated olefins has been used at 3712 Å and 22°C to determine the quenching rate constants of the reaction \documentclass{article}\pagestyle{empty}\begin{document}${\rm SO}_{\rm 2} ({}^3B_1){\rm M}\mathop \to \limits^{k_{_4}}$\end{document} removal. With PSo2 = 25.4 torr and Pcis‐C2F2H2 = 0.239 torr Stern–Volmer plots for M = C2H4, C2H2F, 1,1‐C2F2H2, C2F4, and C3F6 yielded k4 (units of 1010 l./mole · sec) values of 5.29 ± 0.16, 4.21 ± 0.53, 1.92 ± 0.23, 0.575 ± 0.060, and 0.0335 ± 0.0027, respectively. The results were consistent with the ability of an olefin to quench SO2(3B1) being inversely proportional to the polarizability of the olefin's π bond and the effect can be clearly noted as each H atom in C2H4 is individually replaced by an F atom.