Free Band Research Articles

Polynomial time multiplication and normal forms in free bands

We present efficient computational solutions to the problems of checking equality, performing multiplication, and computing minimal representatives of elements of free bands. A band is any semigroup satisfying the identity x2≈x and the free bandFB(k) is the free object in the variety of k-generated bands. Radoszewski and Rytter developed a linear time algorithm for checking whether two words represent the same element of a free band. In this paper we describe an alternate linear time algorithm for the same problem. The algorithm we present utilises a representation of words as synchronous deterministic transducers that lend themselves to efficient (quadratic in the size of the alphabet) multiplication in the free band. This representation also provides a means of finding the short-lex least word representing a given free band element with quadratic complexity.

Blending of Floating Car Data and Point-Based Sensor Data to Deduce Operating Speeds under Different Traffic Flow Conditions

Nowadays, smart mobility can rely on innovative tools for the knowledge of road system conditions, like operating speed data extracted from the so-called Floating Car Data (FCD). Probe vehicles in the traffic flow send to operation centres a large amount of travel information, collected through GPS detection systems, especially with regard to geolocation, date and time, direction and speed. As the sample deriving from these vehicles represents a tiny portion of the entire vehicular fleet, in this paper an analysis and a comparison with data obtained by point-based traffic sensors is proposed. Therefore, the study analyses data collected by inductive loop detectors and microwave radar sensors, that provide information on the entire traffic flow in the time domain, in particular with the aim to identify free flow speed time bands. Afterwards, by means of the fusion between the results obtained from the data coming from these point-based control units and the ones coming from the probe vehicles, a comparison of the operating speeds in the two conditions of constrained and unconstrained traffic flow is performed.

Glass formation and topology in relation to free volume, glass transition and band structure in Ge-Se-Sb chalcogenide system

The algebraic criterion for glass formation and glass stability has been discussed in terms of the mechanical threshold and physical parameters like mean bond energy and lone pair electrons of the Ge20Se80-xSbx (x = 0, 4, 8, 12, 16, 20) chalcogenide system. The topological parameter, mean coordination number (<r > ), has been correlated to the free volume percentage, glass transition temperature and theoretical bandgap of the system. Two approaches, namely, Manca's and Shimakawa's, have been used to calculate the theoretical bandgap. A stoichiometric composition at x = 16 has been predicted, and it is concluded that mechanical and chemical thresholds co-exist in the system and that the system is a potential candidate for IR applications.

Schwannoma: Another dermoscopic pitfall?

Schwannoma: Another dermoscopic pitfall?

Study on FR4 substrate backed flaring antenna structure for wideband applications

A class of planar antenna which offers better performance over broad band of frequencies that fits itself in wide range of applications are in need of research. The license free band from 3.1 GHz to 10.6 GHz that do not cause interference to narrowband signals is chosen as operating range of frequencies for the chosen Vivaldi antenna. The novelty of the proposed work consists in the remodeling of a mathematical equations for elliptic antenna structure and the study of the Vivaldi antenna operating over the frequency range between 2.63 GHz to 14.58 GHz that lies in Super High Frequency (SHF) bands – S, C and X bands. The designed antenna is fabricated and its radiation characteristics are studied and analyzed. Purpose. Analysis of the designed antenna on the basis of an elliptical curve mathematical model will allow the antenna to operate over wide band of frequencies thus extending its applications over the areas of application in the areas of satellite communication, military, weather radar, surface ship radar. Methods. The antenna is being designed using HFSS software and fabricated antenna is being tested at anechoic chamber. Results. A mathematical model of a structure of Vivaldi antenna was developed and studied. The performance measures of designed antenna such as return loss, gain, VSWR and radiation pattern are simulated and analyzed. The antenna is being fabricated and tested using vector network analyzer and anechoic chamber. Practical value. The analysis of designed antenna over wide band of frequencies is demonstrated. The further research directions of the designed antenna can be extended for the subsequent implementation of the results in suitable applications.

Engineering carrier density at TiO2 nanotube metasurface with hole reservoir for Enhanced Photo-electrocatalysis

Solar-driven photo-electrocatalysis using semiconductor photoelectrodes offers a promising advance for sustainable and environmental-friendly energy utilization technology. At the same time, the inherent drawbacks of TiO2-based materials, such as limited light absorption and low carrier density, limit their practical applications. Engineering nanoarchitectured photocatalysts is an alternative route tailoring their optical properties, thus increasing light-harvesting efficiencies. Herein, combining electrochemical reduction and selective interface decoration, FeOOH modified reductive TiO2 nanotube arrays (FeOOH@R-TiO2 NTA) with enhanced carrier density and improved photocatalytic activity are developed. The well-aligned NTA endows the metasurface with enhanced light absorption in the photocatalyst. Notably, the electrochemical reduction induces Ti3+ states increases free electron density and conduction band tail (defects levels); the modified FeOOH nano blocks act as hole reservoirs to significantly improve the hole-electron separation. The donor density of 4.57 × 1020 cm−3 is recorded at FeOOH@R-TiO2 NTA metasurface, showing 3 orders of magnitude higher than that of calcinated TiO2 (6.62 × 1017 cm−3). The metasurface is applied to oxidize benzyl alcohol triggered by a LED light irradiation, demonstrating a proof-of-concept application. The improved light absorption, carrier separation, and donor density facilitate the photoelectrochemical oxidation performance of FeOOH@R-TiO2 NTA.

Influence of pre-stretching on the tensile strength, fatigue properties and the in-plane anisotropy in Al-Cu-Li alloy AA2099

The influence of pre-stretching prior to artificial aging on microstructure, tensile properties, and fatigue behavior of AA2099-T8 sheets was investigated. The results showed that increased pre-strain level from 1% to 6% resulted in a more uniform distribution and increasing density of the T1 phase. The localized plastic deformation during pre-stretching led to the formation of dense precipitation bands (DPBs) and precipitation free bands (T1-PFBs) in the sheets with the 1% pre-strain. The non-uniform distribution of the T1 phase with T1-PFBs and DPBs resulted in a decrement in elongation and a strong in-plane anisotropy of tensile properties. An appropriate level of pre-strain should be executed aiming to improve elongation and reduce the tensile anisotropy by promoting a uniform distribution of the T1 phase. In-plane anisotropy of yield strength due to the presence of DPBs and T1-PFBs was quantitatively analyzed by the modified Hall-Petch formula. The results of the calculation for the modified model showed good agreement with the experiment. In addition, resistances of fatigue crack propagation (FCP) in the same orientation were gradually decreased with the increment of pre-strain due to the increment in yield strength and more uniform distribution of the T1 phase. For the in-plane anisotropy of FCP resistance, the main reasons were the development of rough fracture surfaces and the transgranular fracture modes in L-T orientation.

Optical properties of InI3: Density functional theory calculations and experimental results

The electronic and optical properties of InI3 have been investigated by both experimental and theoretical approaches. The First Principle electronic structure and optical properties were calculated by Density Functional Theory (DFT) formalism using Full Potential Linearized Augmented Plane Wave plus local orbitals (FP-LAPW + lo) implementing different appropriate exchange-correlation functionals in WIEN2k code. The calculations were also carried out implementing other functionals and only TB-mBJ results tally the closest with experimental results. The optical measurements of a well characterized InI3 films indicate the band gap as of direct type and residual strain dependant. The stress free intrinsic band gap Eg = 2.8 eV (average of Eg⊥c and EgIIc) has been determined from the residual strain dependence of the band gap in closest agreement with theoretically calculated value of 2.9 eV. Both theory and experiment show that the band gap is anisotropic along and perpendicular to c-axis. The electron effective mass me*=0.79m0 and the hole effective mass mh*=0.85m0 have been determined from the band structure. The experimental and theoretical optical properties match reasonably well.

Probing Excitonic Rydberg States by Plasmon Enhanced Nonlinear Optical Spectroscopy in Monolayer WS2 at Room Temperature.

The optoelectronic properties of two-dimensional (2D) transition metal dichalcogenide (TMDC) monolayers such as WS2 are largely dominated by excitons due to strong Coulomb interactions in these 2D confined monolayers, which lead to formation of Rydberg-like excitonic states below the free quasiparticle band gap. The precise knowledge of high order Rydberg excitonic states is of great importance for both fundamental understanding such as many-electron effects and device applications such as optical switching and quantum process information. Bright excitonic states could be probed by linear optical spectroscopy, while probing dark excitonic states generally requires nonlinear optical (NLO) spectroscopy. Conventional optical methods for probing high-order Rydberg excitonic states were generally performed at cryogenic temperatures to ensure enough signal-to-noise ratio (SNR) and narrow line width. Here we have designed a hybrid nanostructure of monolayer WS2 integrated with a plasmonic cavity and investigated their NLO properties at the single particle level. Giant enhancement in NLO responses, stronger excitonic resonance effects, and narrowed line widths of NLO excitation spectra were observed when monolayer WS2 was placed in our carefully designed plasmonic cavity. Optimum enhancement of 1000-, 3000-, and 3800-fold were achieved for two-photon photoluminescence (2PPL), second harmonic generation (SHG), and third-harmonic generation (THG), respectively, in the optimized cavity structure. The line width of SHG excitation spectra was reduced from 43 down to 15 meV. Plasmon enhanced NLO responses brought improved SNR and spectral resolution, which allowed us to distinguish discrete excitonic states with small energy differences at room temperature. By using three complementary NLO techniques in combination with linear optical spectroscopy, energies of Rydberg excitonic states of A (1s, 2s, 2p, 3s, 3p, 4s), B (1s), and C and D excitons of monolayer WS2 have been accurately determined, which allow us to determine exciton binding energy and quasiparticle bandgap. It was interesting to find that the 2p lies 30 meV below 2s, which lends strong support to the theoretical prediction of nonlocal dielectric screening effects based on a non-hydrogenic model. Our results show that plasmon enhanced NLO spectroscopy could serve as a general method for probing high order Rydberg excitonic states of 2D materials.

Research and Application of Computer Collaborative Spectrum Sensing Guided by Radio Technology

Currently, due to the proliferation of smart appliances and the rapid development of wireless communication technologies, there is a huge shortage of spectrum resources. Cognitive radio utilizes technologies that dramatically increase the utilization of free frequency bands, detecting the environment in real time and maximizing the reallocation of spectrum resources by sensing and reallocating the licensed free frequency bands. The frequency and accuracy required to determine the free bands is an important basis for determining the spectrum awareness in all aspects of a sensing radio system. Therefore, for the more complex network environment in reality and the intrusion of malicious users, this paper uses Fast K-medoids and Mean-shift methods for information fusion and an iterative approach to overcome malicious use to fuse data and finally obtain realistic feature statistics. The results show that the collaborative identification strategy proposed in this paper has good results.

Free Phenolic Compounds, Antioxidant Capacity and FT-NIR Survey of Debittered Lupinus mutabilis Seeds

Lupinus mutabilis protein-rich seeds must be debittered before consumption. The aim of this research was to assess free phenolic compounds, antioxidant capacity and FT-NIR spectra of flours from debittered seeds of 33 Andean ecotypes of L. mutabilis, and five varieties belonging to L. luteus, L. angustifolius and L. albus, as controls. The free phenolics were quantified by RP-HPLC, while the antioxidant capacity was evaluated spectrophotometrically through the Reducing Power, ABTS, FRAP and DPPH methods. The free phenolics of L. mutabilis were mostly (85.5–99.6%) flavonoids (genistein and genistein derivatives, apigenin, catechin and naringenin). Other compounds, detected in low quantities, were phenylethanoids (tyrosol and tyrosol derivative) and phenolic acids (cinnamic acid derivatives). The highest total free phenolic concentration was observed in H6 INIA BP (1393.32 mg/kg DM), followed by Chacas, Moteado beige, Huánuco and Lircay. The antioxidant capacity of the L. mutabilis ecotypes exceeded that of the controls and was correlated to flavonoids content. Additionally, a relationship between free phenolic compounds and spectral bands was established by FT-NIR, paving the way for a fast, reliable and non-destructive approach to lupin seeds characterisation. Even after debittering, lupin flours maintained high free phenolic concentrations and antioxidant capacity.

Survivable Routing, Spectrum, Core and Band Assignment in Multi-Band Space Division Multiplexing Elastic Optical Networks

The rapid growth in Internet traffic has contributed to the need to expand network transmission capacity. Multi-band (MB) using existing standard single-mode fibers (SMFs) in the free band is an ideal way to increase the capacity of the fiber. However, the introduction of MB has transferred space division multiplexing - elastic optical networks (SDM-EONs) to multi band-SDM-EONs (MB-SDM <strike xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</strike> EONs), and changed routing, spectrum and core assignment (RSCA) problem to the routing, spectrum, core and band assignment (RSCBA) problem. At the same time, it introduces a new issue named stimulated Raman scattering (SRS), which affects transmission quality. Although an expanded fiber can carry more services, a large number of services will be interrupted if a link fails, which will bring huge losses. Therefore, it is necessary to propose a reasonable protection strategy to ensure reliable transmission quality. In this paper, the survivable RSCBA problem in MB-SDM-EONs is studied, which copes with link failures and considers SRS in signal-to-noise ratio (SNR) analysis. In order to solve the problem, we propose a band partition protection scheme: working and protection resources are allocated in different frequency bands for increasing SNR in a fault-free network. We formulate this problem and band partition protection scheme as an integer linear programming (ILP) model, which takes into account inter-core crosstalk and SNR analysis. Furthermore, a heuristic algorithm based on genetic algorithm is proposed for large-scale networks. We evaluate the performance of the proposed approaches through experimental simulation. The results demonstrate that both proposed approaches are effective in finding the optimal solutions.

Effects Of Physiotherapy on Strength, Range and Function in Children with Erb’s Palsy; An Experimental Study

Children who sustain brachial plexus injuries after birth face significant functional limitations due to a variety of sequelae affecting the shoulder, elbow, or forearm. These effects could be permanent or temporary. It is critical for proper joint development to maintain complete passive mobility while neurological function is being restored. Children with Erb’s palsy are more likely to have weak muscles, which can be found by ultrasonography Objective: To determine the effects of physiotherapy on strength, range and function in children with Erb’s palsy. Methods: It was a clinical trial conducted at physiotherapy department outpatient at General hospital Lahore. A sample of 46 children aged between 0-10 years, with the C5 and C6 lesion and with limited range of motion were included while children with any history of previous or recent trauma or surgery to upper limb and to the other roots of brachial plexuses was excluded. Modified Mallet scale and active movement scale was used as outcome measures. The coin toss technique of randomization was adopted, with 'Heads' assigned to strengthening exercises and 'Tails' assigned to general treatment. Independent sample test was employed to assess pre and post differences. Physiotherapy treatments included neurodevelopmental approaches to improve proprioception input, orthosis, and electrical current stimulation. Free weights, resistance bands and manual resistance were used in the strength training. The active range of motion was evaluated using goniometry, and a baseline measurement was generated using a modified mallet scale. The treatment was given every day for six months. Post-intervention measures were implemented two, four, and six months following the intervention. SPSS 25.0 was used for data analysis. Results: The finding showed that pre-interventional oxford scale muscle strength for experimental group showed the mean and standard deviation (1.434± 0.5068), control group (1.65± 0.48) while Oxford scale muscle strength post intervention showed the results with the mean and standard deviation for the experimental group 3.13± 0.54 and control group 2.65± 0.48 and showed significant p value less than 0.005. Conclusions: The study concluded that physiotherapy integrated approach improved upper limb strength, ranges and functional abilities in patients with Erb’s Palsy.

Emergent Weyl fermions in an orbital multipolar ordered phase

Multipolar orderings in degenerate orbital systems offer unique opportunities for emergent topological phases. The phase diagram of interacting spinless fermions in a $p$-band diamond lattice at unit filling is first studied to elucidate the essential role of orbital multipolar orderings in the evolution of multifold degenerate band nodes. The free band structure around the Brillouin zone center is described by two quadratic band nodes each with a threefold degeneracy, which are spanned by the bonding and antibonding $p$-orbital multiplets, respectively. Upon switching on interactions, the triply degenerate band node is split into a pair of Weyl fermions with opposite chirality due to the onset of orbital multipolar orderings. Further raising interactions ultimately drives the system into an insulating phase with the orbital quadrupolar ordering. Our study is then generalized to spin-$\frac{1}{2}$ fermions, which has direct relevance with solid-state materials. The system develops full spin polarization through a ferromagnetic transition at tiny interactions, leaving the remaining orbital sector activated. The ensuing transitions take place in the orbital sector as a natural consequence, qualitatively recovering the phase diagram of spinless fermions. Our findings shed light on the realization of emergent fermions with a prospect being a frontier at the confluence of topology, orbital physics, and strong correlation.

A Study of C=O…HO and OH…OH (Dimer, Trimer, and Oligomer) Hydrogen Bonding in a Poly(4-vinylphenol) 30%/Poly(methyl methacrylate) 70% Blend and its Thermal Behavior Using Near-Infrared Spectroscopy and Infrared Spectroscopy.

Inter- and intramolecular hydrogen bonding and their temperature-dependent changes in a poly(4-vinylphenol)/poly(methyl methacrylate)(PVPh 30%/PMMA 70%) blend were investigated using near-infrared (NIR) and infrared (IR) spectroscopy. Band assignments of the fundamentals and first overtones of the OH stretching mode of a free OH group and OH groups in C=O···HO and OH···OH (dimer, trimer, and oligomer) hydrogen bonding of PVPh 30%/PMMA 70% were carried out by comparison between its NIR and IR spectra and comparison with NIR and IR spectra of phenol. The comparison of the NIR spectra of the PVPh 30%/PMMA 70% blend (hereafter, we denote it as PVPh30%) with the corresponding IR spectra reveals that to observe bands arising from the free OH and OH···OH dimer, which is a weaker hydrogen bonding, NIR is better while to investigate bands originating from OH groups in the OH···O=C and OH···OH (oligomer) hydrogen bonds, which are stronger hydrogen bonding, IR is better. Thus, a combination of IR and NIR spectroscopy has provided convincing results for the hydrogen bonding of PVPh30%. The relative intensity of the two bands at 7058 and 6921 cm-1 (I7058/I6921) due to the first overtones of the OH stretching modes of the free OH group and the OH group in the dimer, respectively, increases significantly above 90 °C, which is close to Tg of PVPh. In concomitance with the intensity increase in the relative intensity of the free OH band, the intensity of a band at 1706 cm-1 due to the C=O stretching mode of the C=O···HO hydrogen bond of PVPh30% decreases above 90°C. These results suggest that above the Tg of PVPh the C=O···HO hydrogen bond is broken gradually and that the free OH increases. Of note is that below Tg the intensities of NIR bands due to the OH first overtones of free OH group and OH groups in the OH···OH dimer gain intensity in parallel with temperature increase, and above Tg the intensity of the band derived from the OH···OH group increases linearly much slower than that of the band due to the free OH. Moreover, a band due to an OH···OH oligomer decreases linearly. Hence, it is very likely that the OH···OH oligomers dissociate into free OH groups. Anharmonicity of O-H bonds, which is sensitive to a hydrogen bond, was estimated for the free OH and OH bonds in the C=O···HO and OH···OH (dimer, trimer, and oligomer) hydrogen bonding by comparison between the NIR and IR spectra in the OH stretching band regions.

Impact of coordination ability of the selected anions on tuning the structure of Hg(II) complexes constructed from a neutral dithione ligand: Iodine uptake and DFT theoretical studies

In view to examine the role of coordination potential of the selected anions on architect of complexes, HgL2](ClO4)2 (C1) and [HgL2](PF6)2 (C2) were synthesized with a HgS4 core structure by a flexible sulfur donor (1,1-bis(3-methyl-4-imidazoline-2-thione)methane ligand(L). The C1 was crystalized via a branched tube method in MeOH/H2O as a solvent. They have been characterized by the FT-IR, elemental analysis, X-ray powder diffraction (PXRD), density functional theory (DFT) calculations, and considered for the iodine adsorption experiments. Although MOFs and CPS were extensively being studied, but mono and binuclear complexes were rarely used as an adsorbent for removal of the iodine. Additionally, to probe the impact of anions on the structure of complexes, and iodine uptake properties, C1 and C2 were compared with the published dimeric ones [Hg2L2Cl4](C3) and [Hg2L2Br4](C4) with a HgX2S2 core structure. All complexes showed a good performance in removal of iodine from the pollutants. This was supported by a sharp decrease in the intensity of a band at 523 nm nominated to the π*g(p) (HOMO) → σ*u(p) (LUMO) transitions in the free I2 molecule. The iodine capture performance of the monomeric complexes is substantially different with the dimeric ones. C1and C2 remove more than 99% of iodine molecules in the solution within 2 h, whereas C3 and C4 need 24 h to achieve the equilibrium point. The DFT studies and band gap calculations confirmed a charge transfer transition from each of the complexes to the σ*u(p) (LUMO) of the adsorbed iodine molecules with a lower energy relative to the free I2 band gap. Nonlinear optical responses (NLO) and charge transfer properties of the C1-C4 complexes were inspected by the DFT calculations.

A novel time-slotted LoRa MAC protocol for scalable IoT networks

Long Range (LoRa) networks provide long range, cost-effective and energy-efficient communications by utilizing the free unlicensed ISM band, which makes them appealing for Internet of Things (IoT) applications. However, in high density networks, reliable performance might be hard to achieve due to the nodes’ random-access method. Furthermore, the duty cycle restrictions that are imposed on nodes and gateways transmissions can limit the scalability of the network. More importantly, the duty cycle restrictions that are imposed on the downlink communication from the server to nodes can impose further challenges. Consequently, the server in high density networks might not be able to communicate with all network nodes due to its limited duty cycle. Besides, the server might not be able to send individual controlling packets from server to nodes. One way to mitigate such a limit is to allow nodes autonomously determine their transmission parameters without the need for any downlink transmission from the server. Thus, this paper presents the Sector-Based Time Slotted SBTS-LoRa MAC protocol that allows nodes to determine their transmission parameters autonomously based on their location to the gateway. SBTS-LoRa is targeting large scale networks. Simulation results show that our proposed protocol significantly enhances the scalability and outperforms its counterparts by maximizing throughput without compromising the energy efficiency. Specifically, the average throughput for dense networks was enhanced 14 times compared to the Adaptive Data Rate ADR-LoRaWAN.

Non-Covalent Interactions in Molecular Systems: Thermodynamic Evaluation of the Hydrogen-Bond Strength in Amino-Ethers and Amino-Alcohols.

The intramolecular hydrogen bond (intra‐HB) is one of the best‐known examples of non‐covalent interactions in molecules. Among the different types of intramolecular hydrogen bonding, the NH⋅⋅⋅O hydrogen bond in amino‐alcohols and amino‐ethers is one of the weakest. In contrast to the strong OH⋅⋅⋅N intramolecular hydrogen bond, the strength of the NH⋅⋅⋅O bond can hardly be measured with conventional spectroscopic methods, even for simple amino‐alcohols, since the band belonging to the NH⋅⋅⋅O conformer merges with the free OH band. In this work, we developed a combination of G4 calculations, and a method based on experimental vaporization enthalpies to determine the NH⋅⋅⋅O hydrogen bonding strength. The archetypal compounds for this study are 2‐amino‐1‐ethanol and 3‐amino‐1‐propanol as well as their respective methoxy analogs. Based on these molecules, different series were studied to investigate various factors influencing NH⋅⋅⋅O intra‐HB strength. In the first series, the influence of alkylation near the hydroxy or methoxy group and the amino group in sterically hindered aminoalcohols was examined. In the second series, the influence of alkylation of the amino‐group was investigated. In the third series, the effect of extending the alkyl chain between functional groups was studied.

Low-temperature deposition of Cd1-xZnxTe layers by laser sputtering and their physical properties

CdZnTe films were grown by the method of modulated infrared laser deposition at a substrate temperature Tsub ≤ 1200C from appropriate sources on oriented single-crystal substrates Si, GaAs, InSb in the same technological conditions in one technological cycle. Surface morphology and spectra of low-temperature photoluminescence (T = 4.2K) in the energy range from 1.30 to 1.70 eV were studied. Luminescence spectra were analyzed and presented from three different energy regions: from 1.70 eV to 1.60 eV with exciton emission, from 1.60 eV to 1.55 eV by donor-acceptor transitions (DAP) and region A-centers from 1, 55 to 1.40 eV. The presence in the low-temperature photoluminescence spectra of free exciton bands, excitons on the neutral acceptor and neutral donor, and their phonon replicas on CdZnTe/InSb films testifies to the high structural perfection inherent in materials of detector quality with composition corresponding of the CdZnTe-target.

Temperature effect on charge-state transition levels of defects in semiconductors

Defects are crucial in determining the overall physical properties of semiconductors. Generally, the charge-state transition level (TEL), one of the key physical quantities that determines the dopability of defects in semiconductors, is temperature dependent. However, little is known about the temperature dependence of TEL, and, as a result, almost all existing defect theories in semiconductors are built on a temperature-independent approximation. In this article, by deriving the basic formulas for temperature-dependent TEL, we have established two fundamental rules for the temperature dependence of TEL in semiconductors. Based on these rules, surprisingly, it is found that the temperature dependences of TEL for different defects are rather diverse: it can become shallower, deeper, or stay unchanged. This defect-specific behavior is mainly determined by the synergistic or opposing effects between free energy corrections (determined by the local volume change around the defect during a charge-state transition) and band edge changes (which differ for different semiconductors). These basic formulas and rules, confirmed by a large number of state-of-the-art temperature-dependent defect calculations in GaN, may potentially be widely adopted as guidelines for understanding or optimizing doping behaviors in semiconductors at finite temperatures.