Fine Spectrum Research Articles

The fine spectra of a difference of weighted shift operators acting in some classical sequence spaces

In this paper we investigate the fine spectra, the ergodic properties and the linear dynamics of the operatorC(x)=(−nxn+n(n−1)xn−2)n∈N0,x=(xn)n∈N0∈CN0, and of its formal adjoint C′ acting in the classical sequence spaces s, s′, ω and φ. The operators C and C′ acting in s are conjugate to the one-dimensional Ornstein-Uhlenbeck differential operator Ou=u″−xu′ and to the differential operator O′u=u″+xu′+u acting in S(R), respectively.

Effect of morphology modulation and interface engineering of SnS-MoS2 heterojunction on nonlinear optical response

MoS2 base films with different morphologies were prepared by modulating the magnetron sputtering parameters, and the base films were used to induce the growth of SnS with different structures, forming columnar and worm-like SnS-MoS2 heterojunctions, which were found to have excellent nonlinear absorption properties and their properties could be modulated by the morphology of the films by Z-scanning tests. The tunable morphology and crystalline quality of the films were characterized using scanning electron microscopy, atomic force microscopy and X-ray diffraction techniques and explained using the Stranski-Krastanow growth mechanism. The Raman spectrum of the heterojunction shows the A1g vibrational peak at 320 cm−1 and the appearance of Sn4+ in the X-ray photoelectron spectroscopy confirms the existence of S-Sn-S charge transfer channels between the interfaces. The fine spectra of all the elements in the X-ray photoelectron spectroscopy data as well as the characteristic absorption peaks in the absorption spectra confirm the formation of heterojunctions, and the constructed heterojunctions are determined to be type-II heterojunctions using the method of the core energy level. Heterojunction was determined to be a type-II heterojunction by using the core energy level method. The photoluminescence peak quenching of the heterojunction indicates that there is a process of charge transfer between the interfaces, and the type-II heterostructure of SnS-MoS2 makes the nonlinear absorption performance in the 800 nm band regulated by the morphology of the material. The nonlinear optical absorption coefficient is two orders of magnitude higher than that of the pure materials, and the nonlinear absorption performance of the worm-like SnS-MoS2 heterojunction is superior to that of the columnar SnS-MoS2 heterojunction, which is attributed to the larger interfacial contact area, the better crystalline quality, and the more efficient carrier interfacial transport capability. These tunable type-II SnS-MoS2 heterojunctions with ultrafast nonlinear optical absorption have a positive impact on practical applications such as optical limiter devices and all-optical switching devices.

Covalent Organic Framework-Structured Raman Probes for Ultrasensitive In Vivo Bioimaging.

Organic Raman probes, including polymers and small molecules, have attracted great attention in biomedical imaging owing to their excellent biocompatibility. However, the development of organic Raman probes is usually hindered by a mismatch between their absorption spectra and wavelength-fixed excitation, which makes it difficult to achieve resonance excitation necessary to obtain strong Raman signals. Herein, we introduce a covalent organic framework (COF) into the fine absorption spectrum regulation of organic Raman probes, resulting in their significant Raman signal enhancement. In representative examples, a polymer poly(diketopyrrolopyrrole-p-phenylenediamine) (DPP-PD) and a small molecule azobenzene are transformed into the corresponding COF-structured Raman probes. Their absorption peaks show an accurate match of less than 5 nm with the NIR excitation. As such, the COF-structured Raman probes acquire highly sensitive bioimaging capabilities compared to their precursors with negligible signals. By further mechanism studies, we discover that the crystallinity and size of COFs directly affect the π-conjugation degree of Raman probes, thus changing their bandgaps and absorption spectra. Our study offers a universal and flexible method for improving the signal performance of organic Raman probes without changing their structural units, making it more convenient to obtain the highly sensitive organic Raman probes for in vivo bioimaging.

Wind Tunnel Evaluation of Plant Protection Products Drift Using an Integrated Chemical–Physical Approach

The use of plant protection products (PPPs) has become fundamental to guarantee excellent field productivity. Nevertheless, their usage presents critical issues, such as the quantity of substances used, the relative toxicity, and the contamination of nearby fields caused by atmospheric drift. This study focuses on the characterization of aerosol droplets of PPPs produced by spraying a chemical marker, fluorescein, with an orchard airblast sprayer equipped with conventional hollow cone (HC) and anti-drift air inclusion (AI) nozzles, using a wind tunnel as a controlled environment. A particle/droplet image analysis was employed to study the droplet production of the nozzles, while a liquid chromatography tandem mass spectrometry (HPLC-MS/MS) analysis allowed us to evaluate samples collected using a cascade impactor located at 5 m, 10 m, and 20 m from the emission point. Overall, HC nozzles are very accurate at producing specific drop size distributions (DSDs), while AI nozzles produce a much wider DSD, concentrating the largest part of the distributed volume into droplets of a larger size. The marker concentration was much lower for the AI nozzles compared to the HC nozzles; moreover, the two nozzles show a similar trend in the coarse droplet range, while significantly differing in the fine droplet spectrum.

Local laser heating effects in diamond probed by photoluminescence of SiV− centers at low temperatures

The accurate measurement of thermal conductivity of diamond below 10 K has always been a challenge, mainly due to significant error in temperature sensing using the thermocouple method. Diamond is generally considered to have high thermal conductivity, so little attention has been paid to the laser heating effects. Here, we observed the dynamic redshift and broadening of zero phonon line of silicon-vacancy (SiV−) centers at 4 K. Utilizing the intrinsic temperature response of the fine structure spectra of SiV− as a probe, we confirmed that laser heating effect appears and the temperature rising results from high defect concentration. By simulating the thermal diffusion process, we have estimated the thermal conductivity of around 1 W/(m K), which is a two-order magnitude lower than that of single-crystal diamond. Our results provide a feasible scheme for all-optical non-contact temperature sensing and help to solve the problem of accurate measurement of thermal conductivity at cryogenic temperatures.

Comparative Study of Photonic Platforms and Devices for On-Chip Sensing

Chemical and biological detection is now an indispensable task in many fields. On-chip refractive index (RI) optical sensing is a good candidate for mass-scale, low-cost sensors with high performance. While most literature works focus on enhancing the sensors’ sensitivity and detection limit, other important parameters that determine the sensor’s yield, reliability, and cost-effectiveness are usually overlooked. In this work, we present a comprehensive study of the different integrated photonic platforms, namely silica, silicon nitride, and silicon. Our study aims to determine the best platform for on-chip RI sensing, taking into consideration the different aspects affecting not only the sensing performance of the sensor, but also the sensor’s reliability and effectiveness. The study indicates the advantages and drawbacks of each platform, serving as a guideline for RI sensing design. Modal analysis is used to determine the sensitivity of the waveguide to medium (analyte) index change, temperature fluctuations, and process variations. The study shows that a silicon platform is the best choice for high medium sensitivity and a small footprint. On the other hand, silica is the best choice for a low-loss, low-noise, and fabrication-tolerant design. The silicon nitride platform is a compromise of both. We then define a figure of merit (FOM) that includes the waveguide sensitivity to the different variations, losses, and footprint to compare the different platforms. The defined FOM shows that silicon is the best candidate for RI sensing. Finally, we compare the optical devices used for RI sensing, interferometers, and resonators. Our analysis shows that resonator-based devices can achieve much better sensing performance and detection range, due to their fine Lorentzian spectrum, with a small footprint. Interferometer based-sensors allow engineering of the sensors’ performance and can also be designed to minimize phase errors, such as temperature and fabrication variations, by careful design of the interferometer waveguides. Our analysis and conclusions are also verified by experimental data from other published work.

Neutron spectrum optimization for Cf-252 production based on key nuclides analysis

Curium targets are irradiated in high-flux reactors to produce californium-252 (Cf-252). Thermalized neutron spectrum is favorable for Cf-252 production, so traditional methods deploy moderators around the curium targets to optimize the neutron spectrum. However, using moderators alone cannot achieve fine spectrum optimization, and does not necessarily result in better Cf-252 production. We conducted refined neutron spectrum analysis and optimization research to improve production efficiency further. First, based on analysis of the transmutation chain during Cf-252 production, intermediate nuclides with a significant impact on production efficiency, known as “key nuclides,” are identified. Then, the “fission-absorption ratio” and “direct loss rate” of these intermediate nuclides are quantitatively analyzed to determine the energy regions that have a greater negative impact on the production process. Finally, filter materials are selected to reduce the neutron flux in these energy regions, optimizing the neutron spectrum around the curium targets and increasing yield and conversion rate during Cf-252 production. The neutron spectrum optimization method for Cf-252 production based on key nuclides analysis helps improve the efficiency and economy of Cf-252 production.

Chemical and topological disordering in M23C6 due to irradiation: An atomic-scale observation

To clarify the stability of M23C6 precipitate in steels under irradiation, the chemical and topological disordering behaviors in M23C6 subjected to ion irradiation at elevated temperatures were investigated with the combined application of high-resolution electron microscopy (HREM) and electron energy-loss spectroscopy (EELS). Results show that the duplex structured M23C6 which is the core-crystalline and shell-amorphous was observed in the specimen irradiated at 623 K, nevertheless, no amorphous phase was observed in the specimen irradiated at 673 K. HREM observation confirmed the occurrence of the chemical disordering in irradiated M23C6, and the disordering of W atoms in the M23C6 unit cell was clarified by the peak intensity profile of the atomic column from the HREM image. EELS analyses indicate that no obvious chemical shift was observed by the core-loss spectrum, however, the change in the electron mean free path (λ) due to irradiation was confirmed by the low-loss spectrum, which is related to the formation of both irradiation defects and amorphous phase. It is proposed that the decreased material density upon irradiation is ascribed to the formation of W-vacancy-dominated defect clusters. An obvious change in interatomic distance was not observed in the irradiated M23C6 based on the radical distribution function analysis by extended energy-loss fine structure spectrum. However, the peak intensity decreased by irradiation, confirming the occurrence of chemical and topological disordering, regardless of the carbide being crystalline or amorphous.

Analytical study on the atmospheric absorption properties of fiber lasers in a 1 µm band.

Atmospheric absorption is one of the significant factors influencing the atmospheric propagation efficiency of high-power fiber lasers. Based on typical atmospheric environment parameters, the atmospheric absorption (aerosol and atmospheric molecular absorption) of fiber lasers with different linewidths and center wavelengths in a near 1µm band is numerically calculated. The results show that the atmospheric absorption of common (several nanometer scales) and narrow linewidth (<1n m scale) lasers have distinctly different external characteristics, but the intrinsic mechanisms are interconnected. Due to the high wavelength selectivity of atmospheric molecular absorption, this work focuses on the factors influencing water vapor (main absorbing gas) absorption of different linewidth lasers and the corresponding low absorption region. Based on the fine atmospheric absorption spectra of different types of fiber lasers, the output spectra of fiber lasers can be artificially designed to avoid strong absorption during atmospheric propagation and achieve improved high-energy laser propagation efficiency. The above method provides a partial reference for designing and optimizing the light source parameters of high-power fiber lasers for atmospheric propagation.

Magnetic properties of Cr-doped VO2 thin films in tetragonal phase of rutile and their synchrotron-based electronic structures

The present study is focused on the investigation at 400 K of the tetragonal-rutile phase of Cr-doped VO2 (CVO) thin films grown by pulsed laser deposition. Synchrotron-based x-ray measurements of both the surface-sensitive total electron yield (TEY) and bulk-sensitive total fluorescence yield (TFY) modes were used to investigate the pristine and Cr-doped VO2 (5%, 10%, 20%, and 30% of atomic weight). The structural analysis and purity of the crystalline phase of the as-deposited films are manifested via grazing incidence x-ray diffraction patterns, which confirm the tetragonal-rutile phase. The purity of the phase is also confirmed by the presence of Eg-mode phonons in the Raman spectra and its deconvolution reflects on the oxygen-mediated electronic/vibrational transitional effect. A clear hysteretic behavior obtained through vibrating sample magnetometry strongly suggests the ferromagnetic interaction in the thin films of CVO. The local-electronic property of the samples is examined using x-ray absorption spectroscopy (XAS) in TEY and TFY modes where the difference in the configured helicity photons resulted in the fine spectra of x-ray magnetic circular dichroism (XMCD). XAS and XMCD measurements performed at V L2,3 and Cr L2,3 edges explicitly demonstrate the ferromagnetism in the thin films of CVO. The strong hybridization between V 3d and Cr 3d states with O 2p states is evident from the spectra of the O K-edge, resulting in the onset of the cation-pair formation V5+–Cr3+, which is ferromagnetic by means of double-exchange interaction. The theoretical calculation of density functional theory made upon Vienna ab initio simulation package suggests that CVO is in a mixed state of a ferromagnetic-insulator and a half-metallic ferromagnet.

Ultra-Narrow Bandwidth Microwave Photonic Filter Implemented by Single Longitudinal Mode Parity Time Symmetry Brillouin Fiber Laser.

In this paper, a novel microwave photonic filter (MPF) based on a single longitudinal mode Brillouin laser achieved by parity time (PT) symmetry mode selection is proposed, and its unparalleled ultra-narrow bandwidth as low as to sub-kHz together with simple and agile tuning performance is experimentally verified. The Brillouin fiber laser ring resonator is cascaded with a PT symmetric system to achieve this MPF. Wherein, the Brillouin laser resonator is excited by a 5 km single mode fiber to generate Brillouin gain, and the PT symmetric system is configured with Polarization Beam Splitter (PBS) and polarization controller (PC) to achieve PT symmetry. Thanks to the significant enhancement of the gain difference between the main mode and the edge mode when the polarization state PT symmetry system breaks, a single mode oscillating Brillouin laser is generated. Through the selective amplification of sideband modulated signals by ultra-narrow linewidth Brillouin single mode laser gain, the MPF with ultra-narrow single passband performance is obtained. By simply tuning the central wavelength of the stimulated Brillouin scattering (SBS) pumped laser to adjust the Brillouin oscillation frequency, the gain position of the Brillouin laser can be shifted, thereby achieving flexible tunability. The experimental results indicate that the MPF proposed in this paper achieves a single pass band narrow to 72 Hz and the side mode rejection ratio of more than 18 dB, with a center frequency tuning range of 0-20 GHz in the testing range of vector network analysis, which means that the MPF possesses ultra high spectral resolution and enormous potential application value in the domain of ultra fine microwave spectrum filtering such as radar imaging and electronic countermeasures.

2-D fragmentation-aware RMSA based on the relative flexibility of advance reservation requests in elastic optical networks

With the advantages of fine granularity spectrum allocation (SA) and large capacity, elastic optical networks (EONs) are considered as the most promising development direction of optical network in the future. The emergence of two-dimensional (2-D) fragmentation during dynamic SA of EONs not only reduces the availability of resources but also increases the blocking probability of requests. In addition, the advance reservation (AR) request has the characteristics of resource reservation and time flexibility, which further complicates the fragmentation issue. To solve the above issues, in this paper, a fragmentation-aware routing, modulation and spectrum assignment (RMSA) algorithm for AR requests is proposed. First, delayed resource allocation is developed for AR requests. Second, a resource allocation sorting strategy based on the relative flexibility of requests is proposed. The strategy makes full use of the time characteristics of AR request to determine the allocation order of requests. In addition, from the perspective of the impact on adjacent resources, a 2-D path resource model is introduced to evaluate the impact of 2-D fragmentation from the perspective of resource matching degree and resource connectivity. Moreover, simulation results show that the proposed algorithm is better than the benchmark algorithm in terms of blocking probability, resource utilization and fragmentation rate.

The Relationship between Defending the State and National Character in Technological Development for the Millennial Generation During the COVID-19 Pandemic

Background: We know that the whole world is facing the same problem, namely the COVID-19 pandemic, including Indonesia. The Indonesian government has made every effort to reduce the pace of the COVID-19 pandemic by establishing policies and regulations such as implementing health protocols, and others. Covid-19 is a non-natural disaster that affects all aspects of life including the nation's character. The younger generation or those who are known as millennials as a determinant of the nation's character have an important role during the Covid-19 pandemic. The problem at this time is that millennials live in a modern and instant era that shapes them to be free, individualistic, and active in the field of technology. This has caused the millennial generation to start forgetting their love for the Motherland and Defending the Country. Methods: The method used in this research is descriptive qualitative and the human instrument is the researcher. A descriptive qualitative method in the form of analyzing and drawing conclusions using various sources of literature. Results: In times of peace and war, young intellectuals as the national guard in non-military defense have a crucial role as potential agents of change in shaping the character and character of the nation. The serious challenges faced by the younger generation must also be addressed by maintaining a balance between intellectual intelligence and emotional intelligence as well as spiritual intelligence. It is hoped that the balance of these three factors will manifest the behavior of young people who always uphold morals and ethics of honesty and nationality. This ability is a form of defending the country on a fine spectrum that needs to be carried out by young people in times of peace. From the perspective of national defense, it is precisely this role of defending the country in the soft spectrum that will determine the quality of the nation's defense and resilience in the future. The toughness and tenacity and ability of the nation to develop the potential of national strength to become a solid state defense force need to be built on the values of nationalism and defense of the country. From the perspective of national resilience, these three basic elements are prerequisites that must be fostered early, continuously, integrated and sustainable. Intellectual intelligence which is a great potential possessed by young people must be able to be developed in a balanced way with emotional intelligence, moral intelligence, and spiritual intelligence. During the Covid-19 pandemic, it turned out that the millennial generation showed high concern and made good contributions as a form of defending the country to maintain national resilience and support the Indonesian government in preventing and handling unexpected events such as Covid-19. Conclusion: The existence of social media as a form of technological progress can be used to hold fundraising events which will later be given to underprivileged communities affected by Covid-19 and medical personnel who lack PPE (personal protective equipment). With the urgency of Indonesia's current situation, the younger generation is required to care about using technology as best as possible in an effort to defend the country which is carried out to help the government and show love for the motherland, harmonious relations between the government and its people, and awareness of the obligations of the nation and state.

The ocean fine spray

An important fraction of the atmospheric aerosols comes from the ocean spray originated by the bursting of surface bubbles. A theoretical framework that incorporates the latest knowledge on film and jet droplets from bubble bursting is here proposed, suggesting that the ejected droplet size in the fine and ultrafine (nanometric) spectrum constitutes the ultimate origin of primary and secondary sea aerosols through a diversity of physicochemical routes. In contrast to the latest proposals on the mechanistic origin of that droplet size range, when bubbles of about 10–100 μm burst, they produce an extreme energy focusing and the ejection of a fast liquid spout whose size reaches the free molecular regime of the air. Simulations show that this spout yields a jet of sub-micrometer and nanometric scale droplets whose number and speed can be far beyond any previous estimation, overcoming by orders of magnitude other mechanisms recently proposed. The model proposed can be ultimately reduced to a single controlling parameter to predict the global probability density function of the ocean spray. The model fits remarkably well most published experimental measurements along five orders of magnitude of spray size, from about 5 nm to about 0.5 mm. According to this proposal, the majority of ocean aerosols would have their extremely elusive birth in the collapsing uterus-like shape of small bursting bubbles on the ocean surface.

Some Spectrum Estimates of the $\alpha q$-Ces\`{a}ro Matrices with $0&lt;\alpha ,q&lt;1$ on $c$

$q$-Calculus Theory is rapidly growing in various directions. The goal of this paper is to collect and underline recent results on $\alpha q$-analogs of the Cesàro matrix andemphasize various generalizations. One $\alpha q$-analogs of the Cesàro matrix of order one is the triangular matrix with nonzero entries $c_{nk}^{\alpha }\left( q\right) =\tfrac{\left( \alpha q\right) ^{n-k}}{1+q+\cdots +q^{n}},\ 0\leq k\leq n$, where $\alpha ,q\in \left( 0,1\right) $. The purpose of this article examines various spectral decompositions of $C_{q}^{\alpha }=\left( c_{nk}^{\alpha }\left( q\right) \right) $ such as the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum on the sequence space $c$.

Successive infusion of Mncl2 in order to analyze the image produced by MRI machines

The use of MRI machines is a fast growing in the field of Medical Imaging. MRI machine operates on the principal of Nuclear Magnetic Resonance Imaging which can be explained by Quantum Mechanics or Classical Mechanics. Nuclear Magnetic Resonance Imaging is a process by which atomic nuclei containing protons and neutrons which are all inform of a magnetic field absorb and re-emit electromagnetic radiation. The energy of the emitted electromagnetic radiation is usually at a certain resonance frequency, which depends upon the strength of the magnetic field and the magnetic properties of the atoms. The resonance frequency produced is similar to radio frequency RF radiation, which when observed it produce a fine spectrum of anatomical structure of objects. MRI machines are currently used in hospitals and clinics to take the anatomical structures of the human body. And a wide variety of artifacts is routinely encountered on the images produced by this Machines. Manganese is a metal that was proposed to be use in NMRI machines, but due to it’s toxic nature and it is a heavy metal, it is not use at all. But we are able to produce metallic chloride of Mn2+ which over comes the toxicity of metal and behaves like a metallic Salt in the human body. However, we are able to successfully infuse MnCl2 into a Rat and a Rabbit due to its unique properties in order to analyse the images produced by a MRI Machine. Conclusively, we are able to observe that MnCl2 improves the images quality produced by the MRI Machine.

On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence $c$

The upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ is defined on a Banach sequence space by $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})(x_{n})=(a_{n}x_{n}+b_{n}x_{n+1})_{n=0}^{\infty}$where $a_{x}=a_{y},~b_{x}=b_{y}$ for $x\equiv y~(mod3)$. The class of the operator$U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$includes, in particular, the operator $U(r,s)$ when $a_{k}=r$ and $b_{k}=s$ for all $k\in\mathbb{N}$, with $r,s\in\mathbb{R}$ and $s\neq 0$. Also, it includes the upper difference operator; $a_{k}=1$ and $b_{k}=-1$ for all $k\in\mathbb{N}$. In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence space $c$.

On the fine spectrum of the operator Q(r,s,t,u) over ℓp and bvp, 1&lt;p&lt;∞

We specify the fine spectrum of the quadruple band matrix operator Q(r,s,t,u) over the sequence spaces ℓp and bvp, where 1<p<∞. The quadruple band matrix Q(r,s,t,u) is the general state of Δ3, D(r,0,0,s), B(r,s,t), Δ2, B(r,s), Δ, right shift and Zweier matrices, where Δ3, B(r,s,t), Δ2, B(r,s) and Δ are called third-order difference, triple band, second-order difference, double band (generalized difference) and difference matrix, respectively.

Ultranarrow lines in Raman spectra of quantum wells due to effective acoustic phonon selection by in-plane wave vector

An unusual fine spectrum of very narrow lines ($&lt;1\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ overall) is observed in resonance Raman scattering from a CdTe quantum well under normal light incidence, when the laser excitation is about one longitudinal optical (LO) phonon energy higher than the quantum well exciton ground state. The visibility of this fine spectrum is improved by sample doping which reduces the quantum yield of the exciton photoluminescence. The appearance of the four sideway lines of the fine spectrum is explained by the Raman scattering on the combination of LO and longitudinal acoustic (LA) [transverse acoustic (TA)] phonons with the $e1hh1(2s)$ exciton serving as an intermediate state. The central line is due to elastic scattering of the $2s$ exciton to the hot $1s$-exciton state on a static random potential of the heterostructure followed by emission of a LO phonon.

Photoemission and photofragmentation of butanoic, hexanoic and octanoic acids in the gas phase

The valence and C 1 s core photoelectron spectra of three carboxylic acids (butanoic, hexanoic and octanoic) as well as the near-edge absorption fine structure spectra and photo-electron photo-ion coincidence spectra have been measured. Changes in the valence spectra are related to the lengthening of the aliphatic chains, and the core spectra have been assigned. Small shifts of the carboxylic carbon 1 s binding energy are related to screening of the core hole by the aliphatic group. The C K edge near-edge absorption fine structure spectra probe the unoccupied density of states and the main changes in the spectra are due to increasing length of the aliphatic chain and related Rydberg states. The coincidence spectra show that soft (near threshold) ionization of all compounds leads to parent ion formation for butanoic and octanoic acids. For hexanoic acid, both parent ions and fragments are produced for near threshold ionization. Fragmentation occurs at the C2C3 bond for all carboxylic acids at the lowest energies, and other channels open for higher internal energy.