Comparative analyses of mitogenomes in the social bees with insights into evolution of long inverted repeats in the Meliponini

The insect mitogenome is typically a compact circular molecule with highly conserved gene contents.Nonetheless,mitogenome structural variations have been reported in specific taxa,and gene rearrangements,usually the tRNAs,occur in different lineages.Because synapomorphies of mitogenome organizations can provide information for phylogenetic inferences,comparative analyses of mitogenomes have been given increasing attention.However,most studies use a very few species to represent the whole genus,tribe,family,or even order,overlooking potential variations at lower taxonomic levels,which might lead to some incorrect inferences.To provide new insights into mitogenome organizations and their implications for phylogenetic inference,this study conducted comparative analyses for mitogenomes of three social bee tribes(Meliponini,Bombini,and Apini)based on the phylogenetic framework with denser taxonomic sampling at the species and population levels.Comparative analyses revealed that mitogenomes of Apini and Bombini are the typical type,while those of Meliponini show diverse variations in mitogenome sizes and organizations.Large inverted repeats(IRs)cause significant gene rearrangements of protein coding genes(PCGs)and rRNAs in Indo-Malay/Australian stingless bee species.Molecular evolution analyses showed that the lineage with IRs have lower dN/dS ratios for PCGs than lineages without IRs,indicating potential effects of IRs on the evolution of mitochondrial genes.The finding of IRs and different patterns of gene rearrangements suggested that Meliponini is a hotspot in mitogenome evolution.Unlike conserved PCGs and rRNAs whose rearrangements were found only in the mentioned lineages within Meliponini,tRNA rearrangements are common across all three tribes of social bees,and are significant even at the species level,indicating that comprehensive sampling is needed to fully understand the patterns of tRNA rearrangements,and their implications for phylogenetic inference.

Analysis of Progressively Type-Ⅱ Inverted Generalized Gamma Censored Data and Its Engineering Application

A novel inverted generalized gamma(IGG)distribution,proposed for data modelling with an upside-down bathtub hazard rate,is considered.In many real-world practical situations,when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing,censoring strategies are frequently used.From this point of view,in the presence of censored data compiled from the most well-known progressively Type-Ⅱ censoring technique,this study examines different parameters of the IGG distribution.From a classical point of view,the likelihood and product of spacing estimation methods are considered.Observed Fisher information and the deltamethod are used to obtain the approximate confidence intervals for any unknown parametric function of the suggestedmodel.In the Bayesian paradigm,the same traditional inferential approaches are used to estimate all unknown subjects.Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’findings.Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy.Further,using several optimality criteria,the optimumprogressive censoring design is suggested.To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model,we analyze the failure times of twenty mechanical components of a diesel engine.

Role of self-assembled molecules’anchoring groups for surface defect passivation and dipole modulation in inverted perovskite solar cells

Inverted perovskite solar cells have gained prominence in industrial advancement due to their easy fabrication,low hysteresis effects,and high stability.Despite these advantages,their efficiency is currently limited by excessive defects and poor carrier transport at the perovskite-electrode interface,particularly at the buried interface between the perovskite and transparent conductive oxide(TCO).Recent efforts in the perovskite community have focused on designing novel self-assembled molecules(SAMs)to improve the quality of the buried interface.However,a notable gap remains in understanding the regulation of atomic-scale interfacial properties of SAMs between the perovskite and TCO interfaces.This understanding is crucial,particularly in terms of identifying chemically active anchoring groups.In this study,we used the star SAM([2-(9H-carbazol-9-yl)ethyl]phosphonic acid)as the base structure to investigate the defect passivation effects of eight common anchoring groups at the perovskite-TCO interface.Our findings indicate that the phosphonic and boric acid groups exhibit notable advantages.These groups fulfill three key criteria:they provide the greatest potential for defect passivation,exhibit stable adsorption with defects,and exert significant regulatory effects on interface dipoles.Ionized anchoring groups exhibit enhanced passivation capabilities for defect energy levels due to their superior Lewis base properties,which effectively neutralize local charges near defects.Among various defect types,iodine vacancies are the easiest to passivate,whereas iodine-substituted lead defects are the most challenging to passivate.Our study provides comprehensive theoretical insights and inspiration for the design of anchoring groups in SAMs,contributing to the ongoing development of more efficient inverted perovskite solar cells.

Efficient and Stable Inverted Perovskite Solar Modules Enabled by Solid-Liquid Two-Step Film Formation

A considerable efficiency gap exists between large-area perovskite solar modules and small-area perovskite solar cells.The control of forming uniform and large-area film and perovskite crystallization is still the main obstacle restricting the efficiency of PSMs.In this work,we adopted a solid-liquid two-step film formation technique,which involved the evaporation of a lead iodide film and blade coating of an organic ammonium halide solution to prepare perovskite films.This method possesses the advantages of integrating vapor deposition and solution methods,which could apply to substrates with different roughness and avoid using toxic solvents to achieve a more uniform,large-area perovskite film.Furthermore,modification of the NiO_(x)/perovskite buried interface and introduction of Urea additives were utilized to reduce interface recombination and regulate perovskite crystallization.As a result,a large-area perovskite film possessing larger grains,fewer pinholes,and reduced defects could be achieved.The inverted PSM with an active area of 61.56 cm^(2)(10×10 cm^(2)substrate)achieved a champion power conversion efficiency of 20.56%and significantly improved stability.This method suggests an innovative approach to resolving the uniformity issue associated with large-area film fabrication.

A Nonlinear Explicit Model of A Non-Circular Subsea Tunnel-Liner System with An FGM Inverted Arch Under Mechanical Loading and Fire Fields

This paper proposes an explicit scheme to analyze the failure of a subsea polyhedral tunnel-liner system with an inverted arch under mechanical loading and fire fields.The thin-walled liner is made of Functionally Graded Materials(FGMs),which may improve the stability behavior of the tunnel-liner system.Hydrostatic pressure is inevitable in the liner since underground water may penetrate the cracks of the tunnel,and reach the outer surface of the liner.In addition,an elevated temperature loading is taken into account,considering that fire may occur in the tunnel-liner system.Under the combination of mechanical loading and thermal loading,the liner deforms into a single-lobe shape,which is depicted by a trigonometric function.The total potential energy is expressed quantitatively after the energy approach and thin-walled shell theory are used.The minimum potential energy is obtained when the critical buckling occurs.The critical buckling pressure is calculated,which considers the effect of the thermal field.The present analytical prediction is subsequently compared precisely with other closed-form solutions.Finally,the effects of several parameters,such as the geometric shapes,temperature variations,and volume fraction indices,are discussed to further survey the buckling performance of the nonlinear buckling of an FGM polyhedral liner with an inverted arch.One may address a polyhedral liner with fewer polyhedral sides,and a lower volume fraction index is recommended to rehabilitate cracked tunnels in engineering applications.

Non-destructive buffer enabling near-infrared-transparent inverted inorganic perovskite solar cells toward 1400 h light-soaking stable perovskite/Cu(In,Ga)Se_(2) tandem solar cells

Near-infrared(NIR)transparent inverted all-inorganic perovskite solar cells(PSCs)are excellent top cell candidates in tandem applications.An essential challenge is the replacement of metal contacts with transparent conductive oxide(TCO)electrodes,which requires the introduction of a buffer layer to prevent sputtering damage.In this study,we show that the conventional buffers(i.e.,small organic molecules and atomic layer deposited metal oxides)used for organic-inorganic hybrid perovskites are not applicable to all-inorganic perovskites,due to non-uniform coverage of the vulnerable layers underneath,deterioration upon ion bombardment and moisture induced perovskite phase transition,A thin film of metal oxide nanoparticles by the spin-coating method serves as a non-destructive buffer layer for inorganic PSCs.All-inorganic inverted near-infrared-transparent PSCs deliver a PCE of 17.46%and an average transmittance of 73.7%between 780 and 1200 nm.In combination with an 18.56%Cu(In,Ga)Se_(2) bottom cell,we further demonstrate the first all-inorganic perovskite/CIGS 4-T tandem solar cell with a PCE of 24.75%,which exhibits excellent illumination stability by maintaining 86.7%of its initial efficiency after 1400 h.The non-destructive buffer lays the foundation for efficient and stable NIR-transparent inverted inorganic perovskite solar cells and perovskite-based tandems.

Control of GaN inverted pyramids growth on c-plane patterned sapphire substrates

Growth of gallium nitride(GaN)inverted pyramids on c-plane sapphire substrates is benefit for fabricating novel devices as it forms the semipolar facets.In this work,GaN inverted pyramids are directly grown on c-plane patterned sapphire substrates(PSS)by metal organic vapor phase epitaxy(MOVPE).The influences of growth conditions on the surface morphol-ogy are experimentally studied and explained by Wulff constructions.The competition of growth rate among{0001},{1011},and{1122}facets results in the various surface morphologies of GaN.A higher growth temperature of 985 ℃ and a lowerⅤ/Ⅲratio of 25 can expand the area of{}facets in GaN inverted pyramids.On the other hand,GaN inverted pyramids with almost pure{}facets are obtained by using a lower growth temperature of 930℃,a higherⅤ/Ⅲratio of 100,and PSS with pattern arrangement perpendicular to the substrate primary flat.

Fast and Balanced Charge Transport Enabled by Solution-Processed Metal Oxide Layers for Efficient and Stable Inverted Perovskite Solar Cells

Metal oxide charge transport materials are preferable for realizing long-term stable and potentially low-cost perovskite solar cells(PSCs).However,due to some technical difficulties(e.g.,intricate fabrication protocols,high-temperature heating process,incompatible solvents,etc.),it is still challenging to achieve efficient and reliable all-metal-oxide-based devices.Here,we developed efficient inverted PSCs(IPSCs)based on solution-processed nickel oxide(NiO_(x))and tin oxide(SnO_(2))nanoparticles,working as hole and electron transport materials respectively,enabling a fast and balanced charge transfer for photogenerated charge carriers.Through further understanding and optimizing the perovskite/metal oxide interfaces,we have realized an outstanding power conversion efficiency(PCE)of 23.5%(the bandgap of the perovskite is 1.62 eV),which is the highest efficiency among IPSCs based on all-metal-oxide charge transport materials.Thanks to these stable metal oxides and improved interface properties,ambient stability(retaining 95%of initial PCE after 1 month),thermal stability(retaining 80%of initial PCE after 2 weeks)and light stability(retaining 90%of initial PCE after 1000 hours aging)of resultant devices are enhanced significantly.In addition,owing to the low-temperature fabrication procedures of the entire device,we have obtained a PCE of over 21%for flexible IPSCs with enhanced operational stability.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

High-Performance and Large-Area Inverted Perovskite Solar Cells Based on NiO_(x) Films Enabled with A Novel Microstructure-Control Technology

The improvement in the efficiency of inverted perovskite solar cells(PSCs)is significantly limited by undesirable contact at the NiO_(x)/perovskite interface.In this study,a novel microstructure-control technology is proposed for fabrication of porous NiO_(x)films using Pluronic P123 as the structure-directing agent and acetylacetone(AcAc)as the coordination agent.The synthesized porous NiO_(x)films enhanced the hole extraction efficiency and reduced recombination defects at the NiO_(x)/perovskite interface.Consequently,without any modification,the power conversion efficiency(PCE)of the PSC with MAPbl_(3)as the absorber layer improved from 16.50%to 19.08%.Moreover,the PCE of the device composed of perovskite Cs0.05(MA_(0.15)FA_(0.85))_(0.95)Pb(I_(0.85)Br_(0.15))_(3)improved from 17.49%to 21.42%.Furthermore,the application of the fabricated porous NiO_(x)on fluorine-doped tin oxide(FTO)substrates enabled the fabrication of large-area PSCs(1.2 cm^(2))with a PCE of 19.63%.This study provides a novel strategy for improving the contact at the NiO_(x)/perovskite interface for the fabrication of high-performance large-area perovskite solar cells.

Chlorine-Substituent Regulation in Dopant-Free Small-Molecule Hole-Transport Materials Improves the Effi ciency and Stability of Inverted Perovskite Solar Cells

Although doped hole-transport materials(HTMs)off er an effi ciency benefi t for perovskite solar cells(PSCs),they inevi-tably diminish the stability.Here,we describe the use of various chlorinated small molecules,specifi cally fl uorenone-triphenylamine(FO-TPA)-x-Cl[x=para,meta,and ortho(p,m,and o)],with diff erent chlorine-substituent positions,as dopant-free HTMs for PSCs.These chlorinated molecules feature a symmetrical donor-acceptor-donor structure and ideal intramolecular charge transfer properties,allowing for self-doping and the establishment of built-in potentials for improving charge extraction.Highly effi cient hole-transfer interfaces are constructed between perovskites and these HTMs by strategi-cally modifying the chlorine substitution.Thus,the chlorinated HTM-derived inverted PSCs exhibited superior effi ciencies and air stabilities.Importantly,the dopant-free HTM FO-TPA-o-Cl not only attains a power conversion effi ciency of 20.82% but also demonstrates exceptional stability,retaining 93.8%of its initial effi ciency even after a 30-day aging test conducted under ambient air conditions in PSCs without encapsulation.These fi ndings underscore the critical role of chlorine-substituent regulation in HTMs in ensuring the formation and maintenance of effi cient and stable PSCs.

High-Performance Inverted Perovskite Solar Cells with Sol-Gel-Processed Sliver-Doped NiO_(x)Hole Transporting Layer

Nickel oxide(NiO_(x))has been established as a highly efficient and stable holetransporting layer(HTL)in perovskite solar cells(PSCs).However,existing deposition methods for NiO_(x)have been restricted by high-vacuum processes and fail to address the energy level mismatch at the NiO_(x)/perovskite interface,which has impeded the development of PSCs.Accordingly,we explored the application of NiO_(x)as a hybrid HTL through a sol-gel process,where a NiO_(x)film was pre-doped with Ag ions,forming a p/p^(+)homojunction in the NiO_(x)-based inverted PSCs.This innovative approach offers two synergistic advantages,including the enlargement of the built-in electric field for facilitating charge separation,optimizing energy level alignment,and charge transfer efficiency at the interface between the perovskite and HTL.Incorporating this hybrid HTL featuring the p/p^(+)homojunction in the inverted PSCs resulted in a high-power conversion efficiency(PCE)of up to 19.25%,significantly narrowing the efficiency gap compared to traditional n-i-p devices.Furthermore,this innovative strategy for the HTL enhanced the environmental stability to 30 days,maintaining 90%of the initial efficiency.

Interface engineering of inverted wide-bandgap perovskite solar cells for tandem photovoltaics

Wide-bandgap perovskite solar cells(WBG PSCs)have garnered significant research attention for their potential in tandem solar cells.However,they face challenges such as high open-circuit voltage losses and severe phase instability.These issues are primarily owing to the formation of defects,ion migration,and energy level mismatches at the interface of WBG perovskite devices.Meanwhile,inverted PSCs demonstrate superior stability potential and compatibility with tandem devices,making them the most promising application for WBG perovskite materials.Consequently,interface modulation for such devices has become imperative.In this review,from the perspective of applicability in tandem devices,we first provided a concise overview of WBG perovskite research and its efficiency progress in inverted devices.We further discussed interface carrier dynamics and the potential impact of interfaces on such device performance.Afterward,we presented a comprehensive summary of interface engineering in inverted WBG perovskite(1.60 eV-1.80 eV)solar cells.The research particularly explored both the upper and buried interfaces of WBG absorbers in the inverted PSCs,thoroughly investigating interface design strategies and outlining promising research directions.Finally,this review provides insight into the future development of interface engineering for high-performance and large-area WBG PSCs.

Efficiency enhancement to 24.62%in inverted perovskite solar cells through poly(ionic liquid)bulk modification

Small-molecule ionic liquids(ILs)are frequently employed as efficient bulk phase modifiers for perovskite materials.However,their inherent characteristics,such as high volatility and ion migration properties,pose challenges in addressing the stability issues associated with perovskite solar cells(PSCs).In this study,we design a poly(IL)with multiple active sites,named poly[4-styrenesulfonyl(trifluoromethylsulfonyl)imide]pyri-dine(P[STFSI][PPyri]),as an efficient additive of perovskite materials.The S=O in the sulfonyl group chelates with uncoordinated Pb^(2+)and forms hydrogen bonds with the organic cations in the perovskite,suppressing the volatilization of the organic cations.The N+in pyridine can fix halide ions through electrostatic interaction with I-and Br-ions to prevent halide ion migration.P[STFSI][PPyri]demonstrates the ability to passivate defects and suppress nonradiative recombination in PSCs.Additionally,it facilitates the fixation of organic and halide ions,thereby enhancing the device’s stability and photoelectric performance.Consequently,the introduction of P[STFSI][PPyri]as a dopant in the devices resulted in an excellent efficiency of 24.62%,demonstrating outstanding long-term operational stability,with the encapsulated device maintaining 87.6%of its initial effi-ciency even after 1500 h of continuous maximum power point tracking.This strategy highlights the promising potential of poly(IL)as an effective additive for PSCs,providing a combination of high performance and stabil-ity.

The pathology of urinary bladder lesions with an inverted growth pattern

Inverted lesions in the urinary bladder have been the source of some difficulty in urological pathology. The two common ones are von Brunn＇s nests and cystitis cystic/cystitis glandularis, which are considered normal variants of urothelium. Apart from them, a number of other rare urothelial lesions with inverted growth pattern occur in the urinary bladder. Some of them are only reactive conditions, just as pseudocarcinomatous hyperplasia. Some are benign tumors, namely inverted papilloma. Whereas others are malignant neoplasms, including inverted papillary urothelial neoplasm of low malignant potential （PUNLMP）, non-invasive inverted papillary urothelial carcinoma （low-grade and high-grade）, and invasive urothelial carcinoma （inverted, nested and big nested variants）. Because of the overlapping morphological features of all the inverted lesions mentioned above, even between high-grade invasive carcinoma and psendoearcinomatous hyperplasia which are only a kind of reactive conditions, it is very important for the surgical pathologist to recognize and be familiar with these inverted lesions in urinary bladder. In this article, we review these spectrums of inverted lesions of the urinary bladder. Emphasis is placed on histogenesis, morphology, differential diagnosis of these lesions, and the pathologic grading of the non-invasive inverted neoplasms, such as inverted papilloma, inverted PUNLMP, non-invasive inverted papillary urothelial carcinoma with low-grade, and non-invasive inverted papillary urothelial carcinoma with high-grade.

Analysis of a Wenzhou-Hitting Exceptionally Strong Rainstorm Associated with a Typhoon Inverted Trough in September,1999

Using T106 numerical products, MM5 simulations in conjunction of Q-vector scheme-computed NCEP results, observations and satellite cloud images, study is undertaken for an exceptionally intense rainstorm event afflicting the Wenzhou region of Zhejiang province far away from the tropical storm center happening early on the morning of September 4, 1999 （TS9909 hereinafter）. Evidence suggests that, like previously-studied typhoons landing in autumn south of Xiamen to the eastern part of Guangdong, TS9909 has an inverted trough in the central south of the coastal belt of Zhejiang province that produces the rainstorm from the meso convective complex （MCC） on the warm, moist shear inside; the time and order of the magnitude of the rainfall are bound up with the development of the pattern of strong Q-vector divergence gradients during the event for the study area; the NE - SW coastline and the unique topography of the Yandang mountains inside the region are favorable for air lifting are the major contributors to the torrential rains.

Modeling and Analysis of Variable Frequency Inverted Sine PWM Technique for a Hybrid Cascaded Multilevel Inverter

In cascaded H-bridge multilevel inverter, a variable frequency inverted sine PWM technique is modeled for hybrid electric vehicles. It has a particular advantage of increasing power which is achieved using series connection of H-bridge and also this topology is capable to produce superior spectral quality with considerable improvement of fundamental voltage. The variable frequency inverted sine PWM technique produces lesser torque ripple and enhances the fundamental output voltage mainly at lower modulation index ranges. The topologies of multilevel inverter are flying capacitor, diode clamped and cascaded inverter. In the paper, we will discuss about the cascaded multilevel inverter based on inverted sine PWM technique. The two switching strategies widely used to control multilevel inverters are constant frequency inverted sine PWM (CF-ISPWM) and variable frequency inverted sine PWM (VF-ISPWM). This implies that switch utilization substantially reduces 32.35% of the constant frequency inverted sine PWM switching technique. The performance of the technique is validated in terms of Total Harmonic Distortion (THD) and Torque ripple which significantly reduces when compared to constant frequency ISPWM. The analysis of conventional triangular PWM inverter and inverted sine PWM inverter using constant and variable switching scheme is done in MATLAB Simulink and verified experimentally by FPGA Spartan 3E processor.

Calibration of Soil Electromagnetic Conductivity in Inverted Salinity Profiles with an Integration Method

Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.

Numerical Study of a Novel Procedure for Installing the Tower and Rotor Nacelle Assembly of Offshore Wind Turbines Based on the Inverted Pendulum Principle

Current installation costs of offshore wind turbines(OWTs) are high and profit margins in the offshore wind energy sector are low, it is thus necessary to develop installation methods that are more efficient and practical. This paper presents a numerical study(based on a global response analysis of marine operations) of a novel procedure for installing the tower and Rotor Nacelle Assemblies(RNAs) on bottom-fixed foundations of OWTs. The installation procedure is based on the inverted pendulum principle. A cargo barge is used to transport the OWT assembly in a horizontal position to the site, and a medium-size Heavy Lift Vessel(HLV) is then employed to lift and up-end the OWT assembly using a special upending frame. The main advantage of this novel procedure is that the need for a huge HLV(in terms of lifting height and capacity) is eliminated. This novel method requires that the cargo barge is in the leeward side of the HLV(which can be positioned with the best heading) during the entire installation. This is to benefit from shielding effects of the HLV on the motions of the cargo barge, so the foundations need to be installed with a specific heading based on wave direction statistics of the site and a typical installation season. Following a systematic approach based on numerical simulations of actual operations, potential critical installation activities, corresponding critical events, and limiting(response) parameters are identified. In addition, operational limits for some of the limiting parameters are established in terms of allowable limits of sea states. Following a preliminary assessment of these operational limits, the duration of the entire operation, the equipment used, and weather-and water depth-sensitivity, this novel procedure is demonstrated to be viable.

Shortcut Procedure for Inverted Batch Distillation Column (I) Multicomponent Ideal System

Inverted batch distillation column(stripper) is opposed to a conventional batch distillation col-umn(rectifier). It has a storage vessel at the top and products leave the column at the bottom. The batch stripper is favourable to separate mixtures with a small amount of light components by removing the heavy components as bottom products. In this paper, we are presenting a shortcut procedure based on our earlier work for design and simulation of the inverted batch distillation column, which is equivalent to the Fenske-Underwood-Gilliland procedure for continuous distillation. Given a separation task, we propose to compute the minimum number of stages(Nbmin) and the minimum reboil ratio(Rbmin) required in a batch stripper,which are the stages and reboil ratio required in a hypothetical inverted batch distillation column operating in total reboil ratio or having an infinite number of stages, respectively. Then, it is shown that the performance of inverted batch columns with a finite number of stages and reboil ratios could be correlated in Gilliland coordinates with the minimum stages Nbmin and the minimum reboil ratio Rbmin.