Simple Spectrum Research Articles

Exact solvable family of discrete Schrödinger operators with long-range hoppings

It is shown that one-dimensional discrete Schrödinger operators, with a uniform electric field and long-range hoppings, form an isospectral family with discrete and simple spectrum (and isospectral operators with eigenfunctions having different decay properties). Explicit relations between hopping decay rates and eigenvectors decay rates are obtained. Small perturbations of exponentially decay hopping operators preserve dynamical localization.

Insights into the Structure and Dynamics of Proteins from 19F Solution NMR Spectroscopy.

19F NMR spectroscopy has recently witnessed a resurgence as an attractive analytical tool for the study of the structure and dynamics of biomolecules in vitro and in cells, despite reports of its applications in biomolecular NMR since the 1970s. The high gyromagnetic ratio, large chemical shift dispersion, and complete absence of the spin 1/2 19F nucleus from biomolecules results in background-free, high-resolution 19F NMR spectra. The introduction of 19F probes in a few selected locations in biomolecules reduces spectral crowding despite its increased line width in comparison to typical 1H NMR line widths and allows rapid site-specific measurements from simple 1D spectra alone. The design and synthesis of novel 19F probes with reduced line widths and increased chemical shift sensitivity to the surrounding environment, together with advances in labeling techniques, NMR methodology, and hardware, have overcome several drawbacks of 19F NMR spectroscopy. The increased interest and widespread use of 19F NMR spectroscopy of biomolecules is gradually establishing it as a sensitive and high-resolution probe of biomolecular structure and dynamics, supplementing traditional 13C/15N-based methods. This Review focuses on the advances in 19F solution NMR spectroscopy of proteins in the past 5 years, with an emphasis on novel 19F tags and labeling techniques, NMR experiments to probe protein structure and conformational dynamics in vitro, and in-cell NMR applications.

Intrapulse Spectral Evolution in Photospheric Gamma-Ray Bursts

Photons that decouple from a relativistic jet do so over a range of radii, leading to a spreading in arrival times at the observer. Therefore, changes to the comoving photon distribution across the decoupling zone are encoded in the emitted signal. In this paper, we study such spectral evolution occurring across a pulse. We track the radiation from the deep subphotospheric regions all the way to the observed time-resolved signal, accounting for emission at various angles and radii. We assume a simple power-law photon spectrum injection over a range of optical depths and let the photons interact with the local plasma. At high optical depths, we find that the radiation exists in one of three characteristic regimes, two of which exhibit a high-energy power law. Depending on the nature of the injection, this power law can persist to low optical depths and manifest itself during the rise time of the pulse with a spectral index β ≈ α − 1, where α is the low-energy spectral index. The results are given in the context of a gamma-ray burst jet, but are general to optically thick, relativistic outflows.

Effects of anions on the electrospray ionization of proteins in strong acids.

The effect of anions on the positive electrospray ionization (ESI) of proteins in different strong acids with varying pH values from 3 to 1 is studied using high-pressure ESI. Reducing the pH from ∼2 to 1 caused a drastic shift in charge state from a high-charge-state distribution (HCSD) to a narrow low-charge-state distribution (LCSD). The shift in charge state was consistent with the circular dichroism result that showed a conformational change due to the "acid-induced folding" of proteins from an unfolding state to a compact molten globule state. Acids of different anions produced noticeable differences in the average charge for HCSD and LCSD. For HCSD, the average charge was lower than the value typically observed using formic and acetic acids. As for LCSD, the average charge was lower than the "native" charge. The high abundance of acid anion that induces the protein compaction was believed to play a role in charge reduction. The effectiveness of anions to "refold" a highly unfolded protein to a compact state and the propensity to reduce the charge of HCSD for proteins appeared to follow the selectivity series of anions towards the stationary phase in ion chromatography. However, the propensity of anions to reduce the charge for LCSD follows quite an opposite trend. The presence of ammonium salt in the acidic solution was found to increase the charge of LCSD. The simple mass spectrum with a narrow distribution of charge state obtained with perchloric acid at pH 1 was demonstrated to facilitate the counting of basic sites.

Modeling aerosol transmission spectra from n(λ) and k(λ) infrared optical constants measurements of organic liquids and solids

The effects of light scattering and refraction play significantly different roles for aerosols than for bulk materials, making it challenging to identify aerosolized chemicals using traditional spectral methods or spectral reference libraries. Due to a potentially infinite number of particle morphologies, sizes, and compositions, constructing a database of laboratory-measured aerosol spectra is not a practical solution. Here, as an alternative approach, the measured n/k optical vectors of two example organic materials (diethyl phthalate and D-mannitol) are used in combination with particle absorption / scattering theory (Mie theory and FDTD) and the Beer-Lambert law to generate a series of synthetic infrared transmission / scattered light spectra. The synthetic spectra show significant differences versus simple slab transmission spectra, even for small changes in particle size (e.g., 5 vs. 10 µm) for both single particles and ensembles, potentially serving as useful reference data for aerosol sensing. For spherical single particles with diameters of 1 to 10 µm, FDTD simulations predict changes in the magnitudes of spectral shifts and the shapes of the peaks vs. particle size with only small deviations from Mie theory predictions, yet reliably capture the direction of the shifts. Typical spectral peak shifts in the longwave infrared correspond to Δλ ∼0.20 µm (∼34 cm-1) when compared to corresponding slab transmission spectra. Additionally, synthetic spectra generated from the n/k values derived using two different methods (KBr pellet transmission and single-angle reflectance) are compared using the Mie theory model.

Regime shift in a coastal pelagic ecosystem with increasing human-induced nutrient inputs over decades

Human-induced nutrient inputs to global coastal waters are leading to increasing nutrients and escalating eutrophication. However, how aquatic ecosystem functioning responds to these changes remains insufficiently studied. Here we report the long-term changes in the nutrient regime and planktonic ecosystem functioning in the Daya Bay, a typical subtropical semi-enclosed bay experiencing rapid economic and social development for several decades. Time-series (from 1991 to 2018) data with a mostly quarterly resolution were collected to depict long-term changes in dissolved inorganic nutrients and plankton abundances, based on which we constructed simplified abundance size spectra (SASS) and plankton abundance ratios to describe the functioning of the planktonic ecosystem. The results revealed a long-term increase in system productivity but a decrease in integrated energy transfer efficiency of the planktonic ecosystem, with rising concentrations of dissolved inorganic nitrogen (DIN). Shifts in the nutrient regime and planktonic ecosystem functioning were detected at a tipping point or threshold around 2006–2007. The shifts were characterized by abrupt changes in the trends of nutrient (phosphate, ammonia, nitrite) concentrations, nutrient ratios (DIN/phosphate, silicate/phosphate), plankton abundance, and total plankton biomass. Compared to the nutrient regime, the planktonic ecosystem functioning shifted several years later. Overall, this study indicates that the pelagic ecosystem regime can shift significantly in response to long-term increasing input of human-induced nutrients in coastal waters such as the Daya Bay. The regime shifts may have profound implications for fishery production, and ecosystem management in the bay.

Direct detection of monoterpenes in evacuated air atmospheres by glow discharge plasma source for mass spectrometry

Some compounds, including the monoterpenes, are difficult to be analyzed by chemical ionization mass spectrometry (CI-MS) mass spectrometry because of having distinct chemical features of unsaturated bonds in relatively large molecule, which is responsible for occurring fragmentation of molecular ions. A direct detection of monoterpenes, including monocyclic, bicyclic and oxygenated (acyclic), was carried out using a soft plasma ionization (SPI) source combined with a q-mass spectrometer (q-MS). Detectable signals for monoterpenes were examined in an ambient air discharge plasma when varying the discharge parameters, such as discharge pressure (0.4–3.0 kPa) and sample/carrier pressure ratio (R = 5–100%). Furthermore, to consider the ionization reactions in detail, nitrogen gas was also used as the discharge gas (carrier gas). Monoterpenes, including cross-linked bicyclic (α-pinene and β-pinene) and oxygenated (linalool, geraniol, nerol and eucalyptol), in which their simple spectrum patterns can be obtained with little or no fragmentation at an ambient air pressure of several kPa, has successfully conducted by the pulsed dc SPI-MS. To our knowledge, this is the first report demonstrating that the spectrum pattern of monoterpenes could be directly detected without any complicated fragmentation of analyte ions in the SPI source.

Water-bearing properties of high rank coal reservoir and the effect on multiphase methane

Coal reservoirs commonly exhibit the coexistence of gas and water, wherein the distribution of water plays a crucial role in influencing methane storage and transportation. The presence of water affects methane adsorption, and models predicting adsorbed methane that do not account for water conditions can introduce errors, posing challenges in meeting practical production needs. In this study, through a series of centrifugation experiments and nuclear magnetic resonance (NMR) adsorption experiments, the distribution characteristics of bound water and movable water in reservoirs and their influence on multiphase methane were assessed. The results indicate that under water-bearing conditions, there exists specific methane in the adsorption space, exhibiting properties similar to free methane. In terms of the relaxation characteristics, the presence of water affects both the peak area and morphology of the T2 spectra of multiphase methane. Based on the NMR response characteristics of adsorbed methane at different water saturations, we proposed and established a theoretical model for predicting the content and density of adsorbed methane under varying water saturations. Additionally, utilizing two-dimensional NMR technology, a simple identification spectrum for multiphase methane was established. The study suggests that the presence of water delays the time of adsorption equilibrium for methane. At low water saturations, water primarily inhibits the adsorption rate of methane. However, with increasing pressure and water saturation, water predominantly suppresses the adsorption capacity of methane. At low water saturations, the bound water has a significant effect on adsorbed methane. Conversely, as water saturations increase, movable water gradually occupies adsorption sites with weaker adsorption potential. It is worth noting that with an increase in water saturation, the content of adsorbed methane decreases, but the adsorption phase density may not necessarily decrease. These research findings provide new insights into the interaction mechanisms between water and methane in water-bearing coal reservoirs.

Investigation of structural, photo and thermoluminescence properties of YAGG:Ce nanogarnet for medical dosimetry application

Cerium-doped yttrium aluminum gallium garnet (YAGG:Ce3+) nanophosphors were synthesized using the sol-gel method. Mixed garnet of Y2.97Al5-xGaxO12:Ce0.03 was prepared with varying gallium content: x = 0, 1, 2 and 3 Ga. The effect of gallium substitutions on the structural, photo and thermoluminescence properties of the prepared nanophosphors were studied by X-ray diffraction (XRD), photoluminescence (PL) and thermoluminescence (TL) techniques. XRD results indicated that the single and pure cubic crystal phase was formed for all nanophosphor samples regardless of the Ga content. The PL spectra of all the samples exhibited a green-yellow emission band centered at 522 nm attributed to the 5d → 4f transitions of Ce3+ ions. The TL glow curve spectra recorded after β-particle irradiation showed a strong dependence in terms of position, shape and intensity, of all temperature peaks with the Ga content. The highest TL sensitivity was observed for the sample prepared with x = 2 Ga, with main peak arising at low temperature (85 °C). The sample prepared at x = 1 Ga exhibited also high TL sensitivity with a simple glow curve spectrum showing a main peak at high temperature (∼158 °C). Thus, the linear dose response of this sample has been investigated in the wide dose range from 0.125 to 100 Gy in order to evaluate the potentiality of this material for radiation dosimetry applications.

Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.

Simple Lyapunov spectrum for linear homogeneous differential equations with Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} parameters

In the present paper we prove that densely, with respect to an Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-like topology, the Lyapunov exponents associated to linear continuous-time cocycles Φ:R×M→GL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi :\\mathbb {R}\ imes M\\rightarrow {{\\,\ extrm{GL}\\,}}(2,\\mathbb {R})$$\\end{document} induced by second order linear homogeneous differential equations x¨+α(φt(ω))x˙+β(φt(ω))x=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ddot{x}+\\alpha (\\varphi ^t(\\omega ))\\dot{x}+\\beta (\\varphi ^t(\\omega ))x=0$$\\end{document} are almost everywhere distinct. The coefficients α,β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha ,\\beta $$\\end{document} evolve along the φt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi ^t$$\\end{document}-orbit for ω∈M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega \\in M$$\\end{document} and φt:M→M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi ^t: M\\rightarrow M$$\\end{document} is an ergodic flow defined on a probability space. We also obtain the corresponding version for the frictionless equation x¨+β(φt(ω))x=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ddot{x}+\\beta (\\varphi ^t(\\omega ))x=0$$\\end{document} and for a Schrödinger equation x¨+(E-Q(φt(ω)))x=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ddot{x}+(E-Q(\\varphi ^t(\\omega )))x=0$$\\end{document}, inducing a cocycle Φ:R×M→SL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi :\\mathbb {R}\ imes M\\rightarrow {{\\,\ extrm{SL}\\,}}(2,\\mathbb {R})$$\\end{document}.

Exploring kinetically induced bound states in triangular lattices with ultracold atoms: Spectroscopic approach

Quantum simulations with ultracold fermions in triangular optical lattices have recently emerged as a new platform for studying magnetism in frustrated systems. Experimental realizations of the Fermi Hubbard model revealed striking contrast between magnetism in bipartite and triangular lattices. In bipartite lattices magnetism is strongest at half filling, and doped charge carriers tend to suppress magnetic correlations. In triangular-type lattices for large U/t and t>0, antiferromagnetism (ferromagnetism) gets enhanced by doping away from n=1 with holes (doublons) because kinetic energy of dopants can be lowered through developing magnetic correlations, corresponding to formation of magnetic polarons. Snapshots of many-body states obtained with quantum gas microscopes demonstrated existence of magnetic polarons by revealing the magnetic correlations around dopants at temperatures that considerably exceed superexchange energy scale. In this paper we discuss theoretically that additional insight into properties of magnetic polarons in triangular lattices can be achieved using spectroscopic experiments with ultracold atoms. We consider starting from a spin polarized state with small hole doping and applying a two-photon Raman photoexcitation, which transfers atoms into a different spin state. We show that such magnon injection spectra exhibit a separate peak corresponding to formation of a bound state between a hole and a magnon. This polaron peak is separated from the simple magnon spectrum by energy proportional to single particle tunneling and can be easily resolved with currently available experimental techniques. For some momentum transfer there is an additional peak corresponding to photoexciting a bound state between two holes and a magnon. We point out that in two component Bose mixtures in triangular lattices one can also create dynamical magnetic polarons, with one hole and one magnon forming a repulsive bound state.

Fires in the deep: The luminosity distribution of early-time gamma-ray-burst afterglows in light of the Gamow Explorer sensitivity requirements

Gamma-ray bursts (GRBs) are ideal probes of the Universe at high redshift ($z$), pinpointing the locations of the earliest star-forming galaxies and providing bright backlights with simple featureless power-law spectra that can be used to spectrally fingerprint the intergalactic medium and host galaxy during the period of reionization. Future missions such as Gamow Explorer (hereafter )\ are being proposed to unlock this potential by increasing the rate of identification of high-$z$ ($z>5$) GRBs in order to rapidly trigger observations from $6-10$ m ground telescopes, the James Webb Space Telescope (JWST), and the upcoming Extremely Large Telescopes (ELTs). was proposed to the NASA 2021 Medium-Class Explorer (MIDEX) program as a fast-slewing satellite featuring a wide-field lobster-eye X-ray telescope (LEXT) to detect and localize GRBs with arcminute accuracy, and a narrow-field multi-channel photo-$z$ infrared telescope (PIRT) to measure their photometric redshifts for $>80<!PCT!>$ of the LEXT detections using the Lyman-alpha dropout technique. We use a large sample of observed GRB afterglows to derive the PIRT sensitivity requirement. We compiled a complete sample of GRB optical--near-infrared (optical--NIR) afterglows from 2008 to 2021, adding a total of 66 new afterglows to our earlier sample, including all known high-$z$ GRB afterglows. This sample is expanded with over 2837 unpublished data points for 40 of these GRBs. We performed full light-curve and spectral-energy-distribution analyses of these afterglows to derive their true luminosity at very early times. We compared the high-$z$ sample to the comparison sample at lower redshifts. For all the light curves, where possible, we determined the brightness at the time of the initial finding chart of at different high redshifts and in different NIR bands. This was validated using a theoretical approach to predicting the afterglow brightness. We then followed the evolution of the luminosity to predict requirements for ground- and space-based follow-up. Finally, we discuss the potential biases between known GRB afterglow samples and those to be detected by We find that the luminosity distribution of high-$z$ GRB afterglows is comparable to those at lower redshift, and we therefore are able to use the afterglows of lower-$z$ GRBs as proxies for those at high $z$. We find that a PIRT sensitivity of $15\ (21 mag AB) in a 500 s exposure simultaneously in five NIR bands within 1000s of the GRB trigger will meet the mission requirements. Depending on the $z$ and NIR band, we find that between 75<!PCT!> and 85<!PCT!> of all afterglows at $z>5$ will be recovered by at $5 detection significance, allowing the determination of a robust photo-$z$. As a check for possible observational biases and selection effects, we compared the results with those obtained through population-synthesis models, and find them to be consistent. and other high-$z$ GRB missions will be capable of using a relatively modest 0.3m onboard NIR photo-$z$ telescope to rapidly identify and report high-$z$ GRBs for further follow-up by larger facilities, opening a new window onto the era of reionization and the high-redshift Universe.

Stability of the gapless pure point spectrum of self-adjoint operators

We consider a self-adjoint operator T on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of T and on the bounded perturbation V ensuring the global stability of the spectral nature of T + ɛV, ε∈R.

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) — a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is En ~ log n. Despite the presence of ramps, these sequences do not exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument s = β + it is the Riemann zeta function ζ(s). An immediate consequence is that the spectral form factor is simply −ζ|(it)|2. Our observation that log spectra have a linear ramp, is closely related to the Lindelöf hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through |ζ(it)|2 on a log-log plot is indeed 1, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer N causes the would-be-eternal ramp to end on a plateau.

Fatigue behavior of a nodular cast iron subjected to a variable amplitude strain-based load spectrum applied in bench tests of an Off-highway axle

Nodular cast irons are commonly adopted in off-highway applications, owing to the possibility to shape complex components and to guarantee good mechanical properties. In the fatigue strength assessment of axles made of nodular cast irons, engineers have to deal with external loads that turn into local strain spectra at the fatigue crack initiation zones, which are usually located in areas weakened by notched geometrical details. Moreover, off-highway axles are subjected to variable amplitude load histories during their service life; during the design phase, the field load histories are usually applied to the axles in the form of simplified bench load spectra. In this paper, the mechanical properties of EN-GJS-500-7 have been investigated through static tensile tests and strain-controlled fatigue tests performed on specimens with machined surface extracted from an axle. Furthermore, a local strain-based spectrum has been derived by means of strain gauges which have been applied at the failure location of the axle during the bench tests. Finally, the damage index to failure relevant to the simplified bench load spectrum has been calculated by adopting Miner's linear damage rule and the Smith, Watson and Topper mean stress corrected life equation.

Arc-Induced Electrospray Ionization Mass Spectrometry.

Arc-induced electrospray ionization mass spectrometry (AESI-MS) was developed during which alternating current electrospray is simply achieved through the arc plasma. The AESI source exploits the arc's temperature and charge properties to generate aerosols consisting of charged microdroplets. The electrospray region, in which organic molecules are contained within microdroplets, partially overlaps with the arc plasma region. Guided by the electric field, these molecules undergo ionization, yielding ionic target analytes. AESI represents a soft ionization method that combines the mechanisms of atmospheric pressure chemical ionization and electrospray ionization, facilitating the ionization of analytes with wide ranging polarities. The precisely targeted spraying area enhances ion entry into the mass analyzer, thereby enabling excellent ionization efficiency. The AESI source exhibits several notable advantages over the electrospray ionization source, including an elevated but comparable level of active species concentrations and types, simplified mass spectra for direct amino acid analysis, high salt tolerance, versatile analysis of compounds with varying polarities, and reliable quantitative analysis of amino acids in complex matrices. Overall, AESI broadens the methodologies employed to generate microdroplets, providing a technological and scientific framework for creating distinctive electrospray ionization techniques.

On the eigenvalue-separation properties of real tridiagonal matrices

In this paper, we give a simple sufficient condition for the eigenvalue-separation properties of real tridiagonal matrices T. This result is much more than the statement that the pertinent eigenvalues are distinct. Its derivation is based on recurrence formulae satisfied by the polynomials made up by the minors of the characteristic polynomial det(xE-T) that are proven to form a Sturm sequence. This is a new result, and it proves the simple spectrum property of a symmetric tridiagonal matrix studied in Grünbaum's paper. Two numerical examples underpin the theoretical findings. The style of the paper is expository in order to address a large readership.

Time and band limiting for exceptional polynomials

The “time-and-band limiting” commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones.Here we give a general result that insures the existence of a commuting differential operator for a given family of exceptional orthogonal polynomials satisfying the “bispectral property”. As a main tool we go beyond bispectrality and make use of the notion of Fourier Algebras associated to the given sequence of exceptional polynomials. We illustrate this result with two examples, of Hermite and Laguerre type, exhibiting also a nice Perline's form for the commuting differential operator.

Synthesis, Characterization, and Spectroscopic Studies of 2,6-Dimethylpyridyl-Linked Cu(I)-CNC Complexes: The Electronic Influence of Aryl Wingtips on Copper Centers.

Six new Cu(I) complexes containing pincer ligands of the type 2,6-bis(3-alkyl/arylimidazol-2-ylidene) methylpyridine I(R/R'Ar) ĈN̂C, where R = trifluoroethyl (TFE) and R' = 4-CF3, 4-NO2, 4-CN, 4-H, and 4-CH3, have been synthesized. These complexes, namely, [Cu(I(TFE)ĈN̂C)]PF6, 1-TFE; [Cu(ICF3Ar ĈN̂C]PF6, 2-CF3; [Cu(INO2Ar ĈN̂C)]PF6, 3-NO2; [Cu(ICNAr ĈN̂C]PF6, 4-CN; [Cu(IHAr ĈN̂C)]2(PF6)2, 5-H; and [Cu(ICH3Ar ĈN̂C)]2(PF6)2, 6-CH3, were fully characterized by 1H, 13C, and HMBC NMR spectroscopy, elemental analysis, electrochemical studies, and single-crystal X-ray crystallography. The crystallographic data revealed different structures and copper nuclearities for the complexes bearing aryl wingtips with electron-withdrawing (2-CF3, 3-NO2, and 4-CN) and electron-donating (5-H and 6-CH3) substituents. The solution-phase conductivity measurements in acetonitrile revealed a mix-electrolyte behavior for these complexes, supporting the presence of both mono- and binuclear forms of each complex. The fast monomer-dimer equilibrium of the Cu-CNC complexes at room temperature is reflected in their simple 1H NMR spectra in acetonitrile. However, both mono- and binuclear forms were identifiable in 1H diffusion-ordered spectroscopy (DOSY) at low temperatures. The dynamic behavior of these complexes in solution was further examined by variable-temperature 1H NMR (VT 1H NMR) experiments, and the relevant thermodynamic parameters were determined. The process was also probed by one-dimensional rotating-frame Overhauser enhancement spectroscopy (1D ROESY) experiments to elucidate the coexisting species in solution. The 2,6-dimethylpyridyl-linked Cu-CNC complexes also presented a quasi-reversible Cu(II)/Cu(I) couple in cyclic voltammetry studies, wherein a clear influence of the aryl wingtips on the E1/2 values was observed. Furthermore, the percent buried volumes (% Vbur) of the complexes were calculated, showing a similar steric hindrance around copper in all complexes. These findings support the importance of electronic effects, induced by the aryl wingtips, on the preferred coordination geometry, copper nuclearity, and redox properties of the Cu-CNC complexes.