Improving the performance of 3D image model compression based on optimized DEFLATE algorithm.

This study focuses on optimizing and designing the Delayed-Fix-Later Awaiting Transmission Encoding (DEFLATE) algorithm to enhance its compression performance and reduce the compression time for models, specifically in the context of compressing NX three-dimensional (3D) image models. The DEFLATE algorithm, a dual-compression technique combining the LZ77 algorithm and Huffman coding, is widely employed for compressing multimedia data and 3D models. Three 3D models of varying sizes are selected as subjects for experimentation. The Wavelet algorithm, C-Bone algorithm, and DEFLATE algorithm are utilized for compression, with subsequent analysis of the compression ratio and compression time. The experimental findings demonstrate the DEFLATE algorithm's exceptional performance in compressing 3D image models. Notably, when compressing small and medium-sized 3D models, the DEFLATE algorithm exhibits significantly higher compression ratios compared to the Wavelet and C-Bone algorithms while also achieving shorter compression times. Compared to the Wavelet algorithm, the DEFLATE algorithm enhances the compression performance of 3D image models by 15% and boosts data throughput by 49%. While the compression ratio of the DEFLATE algorithm for large 3D models is comparable to that of the Wavelet and C-Bone algorithms, it notably reduces the actual compression time. Furthermore, the DEFLATE algorithm enhances data transmission reliability in NX 3D image model compression by 12.1% compared to the Wavelet algorithm. Therefore, the following conclusions are drawn: the DEFLATE algorithm serves as an excellent compression algorithm for 3D image models. It showcases significant advantages in compressing small and medium-sized models while remaining highly practical for compressing large 3D models. This study offers valuable insights for enhancing and optimizing the DEFLATE algorithm, and it serves as a valuable reference for future research on 3D image model compression.

Effect of Fiber Content on Mechanical Properties of Fiber-Reinforced CGF All-Solid-Waste Binder-Solidified Soil.

In order to realize the resource utilization of solid waste and improve the tensile strength and toughness of soil, CCR-GGBS-FA all-solid-waste binder (CGF) composed of general industrial solid waste calcium carbide residue (CCR), ground granulated blast furnace slag (GGBS) and fly ash (FA) was used instead of cement and combined with polypropylene fiber to strengthen the silty soil taken from Dongying City, China. An unconfined compressive strength test (UCS test) and a uniaxial tensile test (UT test) were carried out on 10 groups of samples with five different fiber contents to uncover the effect of fiber content on tensile and compressive properties, and the reinforcement mechanism was studied using a scanning electron microscopy (SEM) test. The test results show that the unconfined compressive strength, the uniaxial tensile strength, the deformation modulus, the tensile modulus, the fracture energy and the residual strength of fiber-reinforced CGF-solidified soil are significantly improved compared with nonfiber-solidified soil. The compressive strength and the tensile strength of polypropylene-fiber-reinforced CGF-solidified soil reach the maximum value when the fiber content is 0.25%, as the unconfined compressive strength and the tensile strength are 3985.7 kPa and 905.9 kPa, respectively, which are 116.60% and 186.16% higher than those of nonfiber-solidified soil, respectively. The macro-micro tests identify that the hydration products generated by CGF improve the compactness through gelling and filling in solidified soil, and the fiber enhances the resistance to deformation by bridging and forming a three-dimensional network structure. The addition of fiber effectively improves the toughness and stiffness of solidified soil and makes the failure mode of CGF-solidified soil transition from typical brittle failure to plastic failure. The research results can provide a theoretical basis for the application of fiber-reinforced CGF-solidified soil in practical engineering.

Erratum: A review of auditory processing and cognitive change during normal ageing, and the implications for setting hearing aids for older adults.

[This corrects the article DOI: 10.3389/fneur.2023.1122420.].

A review of auditory processing and cognitive change during normal ageing, and the implications for setting hearing aids for older adults.

Throughout our adult lives there is a decline in peripheral hearing, auditory processing and elements of cognition that support listening ability. Audiometry provides no information about the status of auditory processing and cognition, and older adults often struggle with complex listening situations, such as speech in noise perception, even if their peripheral hearing appears normal. Hearing aids can address some aspects of peripheral hearing impairment and improve signal-to-noise ratios. However, they cannot directly enhance central processes and may introduce distortion to sound that might act to undermine listening ability. This review paper highlights the need to consider the distortion introduced by hearing aids, specifically when considering normally-ageing older adults. We focus on patients with age-related hearing loss because they represent the vast majority of the population attending audiology clinics. We believe that it is important to recognize that the combination of peripheral and central, auditory and cognitive decline make older adults some of the most complex patients seen in audiology services, so they should not be treated as "standard" despite the high prevalence of age-related hearing loss. We argue that a primary concern should be to avoid hearing aid settings that introduce distortion to speech envelope cues, which is not a new concept. The primary cause of distortion is the speed and range of change to hearing aid amplification (i.e., compression). We argue that slow-acting compression should be considered as a default for some users and that other advanced features should be reconsidered as they may also introduce distortion that some users may not be able to tolerate. We discuss how this can be incorporated into a pragmatic approach to hearing aid fitting that does not require increased loading on audiology services.

Difference between Anterior and Posterior Cord Compression and Its Clinical Implication in Patients with Degenerative Cervical Myelopathy.

In degenerative cervical myelopathy (DCM), the low anteroposterior compression ratio of the spinal cord is known to be associated with a neurologic deficit. However, there is little detailed analysis of spinal cord compression. Axial magnetic resonance images of 183 DCM patients at normal C2-C3 and maximal cord compression segments were analyzed. The anterior (A), posterior (P), and anteroposterior length and width (W) of the spinal cord were measured. Correlation analyses between radiographic parameters and each section of Japanese Orthopedic Association (JOA) scores and comparisons of the patients divided by A (below or above 0, 1, or 2 mm) were performed. Between C2-C3 and maximal compression segments, the mean differences of A and P were 2.0 (1.2) and 0.2 (0.8) mm. The mean anteroposterior compression ratios were 0.58 (0.13) at C2-C3 and 0.32 (0.17) at maximal compression. The A and A/W ratio were significantly correlated with four sections and the total JOA scores (p < 0.05), but the P and P/W ratio did not demonstrate any correlations. Patients with A < 1 mm had significantly lower JOA scores than those with A ≥ 1 mm. In patients with DCM, spinal cord compression occurs mainly in the anterior part and the anterior cord length of <1 mm is particularly associated with neurologic deficits.

Numerical Analysis on Dynamic Response of CFRP-Wrapped RC Columns under Lateral Impact Loading.

This paper presents a numerical study examining the dynamic response and resistance mechanism of reinforced concrete (RC) columns strengthened with or without carbon-fiber-reinforced polymer (CFRP) wraps under lateral impact loading by using the software LS-DYNA. First, the information of eight column models was briefly introduced as part of the laboratory experimental program from the literature. Secondly, finite element (FE) models were established in terms of the geometries of impact tests. Then, a detailed comparison between numerical results and experimental results was made, and FE models showed a relatively high simulation accuracy. Subsequently, a series of parametric analyses were carried out with a focus on the effects of axial compression ratio, the boundary condition at the column top, the layer number of CFRP wraps, and the impact velocity and impact height on the dynamic responses of plain and strengthened columns. The results demonstrated that the CFRP retrofit mechanism was not activated during the initial Stage-I when the impact force rapidly increased to the first peak and then decreased to zero. CFRP strengthening came into play in the second stage, Stage-II, and affected the response of the shear force and moment along the column height, as well as had a great influence on the control of shear damage. The dynamic response of RC columns was more sensitive to the impact velocity than to other parameters, regardless of whether CFRP wrapping was applied. The axial compression ratio would have a different influence on the column failure mode if the impact velocity was varied. The variation in impact height and boundary condition at the column top had little influence on the damage mode of strengthened columns.

Experimental analysis on the influence of compression ratio, flow rate, injection pressure, and injection timing on the acetylene - diesel aspirated dual fuel engine.

The predicted scarcity, increasing cost of petroleum fuels, and environmental degradation are encouraging researchers to search for alternative fuels throughout the world. Hence, it is intended to utilize acetylene-based DF in the compression ignition (CI) engine with minor modifications. An engine of 5 Hp, four stroke, single-cylinder, water-cooled operated in dual-fuel (DF) mode (acetylene gas-diesel), aiming to reduce the emissions, was deployed to investigate its characteristics. In DF mode, gaseous fuel is injected through intake air manifold with 2, 4, and 6 lpm constantly. According to the research findings, the gas rate of 6 lpm provides the best results, having a superior BTE of 30.7%. Various compression ratios (16:1, 18:1, and 20:1) were used to determine the optimal compression ratio (CR) under a volume flow rate of 6 lpm with diesel. Fuel injector pressure (200, 220, and 240 bar) with injector intervals (19°, 23°, and 27°bTDC) were changed consecutive sequence while adjusting CR, and the best outcomes for improved CI fuel efficiency were determined. From the investigational analysis, the peak in-cylinder pressure and net HRR (heat release rate) are assessed for being better by the increment in CR in DF mode of operation with an acetylene gas of 6 lpm at all operating settings. At a 240 bar injection pressure, the BTE is recorded highest (35.1%), and smoke was decreased. An IT of 23obTDC, the CO and HC were found as to be minimum as 28 ppm and 0.04 ppm.

Difference in the Cobb Angle Between Standing and Supine Position as a Prognostic Factor After Vertebral Augmentation in Osteoporotic Vertebral Compression Fractures.

OBJECTIVE: We retrospectively analyzed patients with osteoporotic vertebral compression fracture (OVCF) undergoing vertebral augmentation to compare the Cobb angle changes in the supine and standing positions and the clinical outcomes. METHODS: We retrospectively extracted the data of OVCF patients who underwent vertebral augmentation. Back pain was assessed using a visual analogue scale (VAS). Supine and standing radiographs were assessed before treatment to determine the Cobb angle and compression ratio. Receiver operating characteristic curve analysis was performed to determine the optimal cutoff to predict favorable outcomes after vertebral augmentation. RESULTS: A total of 249 patients were included. We observed a statistically significant increase in the VAS score change with increasing Cobb angle and compression ratio (p < 0.001), and multivariate logistic regression analysis showed that a difference in the Cobb angle (odds ratio [OR], 1.27) and compression ratio (OR, 1.12) were the independent risk factors for predicting short-term favorable outcomes after vertebral augmentation. In addition, we found that the difference in the Cobb angle (OR, 1.05) was the only factor for predicting midterm favorable outcomes after vertebral augmentation. The optimal cutoff value of the difference in the Cobb angle for predicting midterm favorable outcomes was 35.526°. CONCLUSION: We found that the midterm clinical outcome after vertebral augmentation was better when there was a difference of approximately 35% or more in the Cobb angle between the standing and supine positions. Surgeons should pay attention to the difference in the Cobb angle depending on the posture when deciding to perform vertebral augmentation in patients with OVCFs.

Impact of compression ratio on combustion, performance and exhaust emissions of diesel engine fueled with Undi methyl ester-diesel and Undi ethyl ester-diesel blends.

The current study emphasizes on the influence of nonedible, easily accessible Undi ester blended diesel in single-cylinder, four-stroke, naturally aspirated, direct-injection variable compression ratio diesel engine. All tests were accomplished by varying volumetric proportions of Undi methyl ester (UME) and Undi ethyl ester by 10%, 20%, 30%, 40%, and 50% and compression ratio (CR) from 16:1-20:1. The Undi esters consolidation to diesel, especially enhances brake thermal efficiency (BTE) and decreases brake specific energy consumption (BSEC) of the engine. In comparison with Diesel, ester fuel blends produce lower unburnt hydrocarbons (UHC), carbon monoxide (CO), and particulate matter (PM) emissions with the cost of higher oxides of nitrogen (NOX). With the increase in compression ratio from 16 to 20. All Undi ethyl ester diesel blends have on an average of 1.44% slightly improved brake thermal efficiency, 1.41% lower brake specific fuel consumption and it emits comparatively on an average 7.90% lesser carbon monoxide, 7.21% lower unburnt hydrocarbon, 0.59% lower particulate matter and 1.94% higher oxides of nitrogen emission than UME diesel blends with an increment in CR from 16 to 20. In addition, ester blends showed higher maximum In-cylinder pressure and heat release rate than commercial diesel. Undi ethyl ester blends show 0.82%, 1.08% on an average higher maximum In-cylinder pressure and heat release rate than UME Diesel blends when CR increased from 16 to 20. Undi ester Diesel blends are found to be utmost substitute to commercial diesel fuel in all features such as combustion, performance and emissions characteristics.

High-fidelity compression for high-throughput photoacoustic microscopy systems.

Photoacoustic microscopic images can assist specialists in disease diagnosis by providing vascular information. However, the size of such data is usually extremely large (ie, gigabytes), and thus, a real-time, efficient compression method can facilitate easy storage and transportation of these images. We have implemented multiple data compression methods in LabVIEW with a high compression ratio and execution times below the repetition rate of the pulsed laser. The qualitative and quantitative results of ex vivo and in vivo imaging with compression showed near-identical images to uncompressed images, with significantly smaller size.

Experimental Study on Seismic Behavior of PC Walls with Alveolar-Type Horizontal Joint under Pseudo-Static Loading.

There are many horizontal joints on precast concrete (PC) wall panel structures, which certainly has a significant impact on the seismic behavior of structures. This paper proposes a novel alveolar-type horizontal joint, which has advantages of convenient and rapid assembly. Six precast concrete wall specimens with alveolar-type joints were designed and constructed, and they were weakly connected by spliced rebars anchored into grouted sleeves to meet the requirements of structural performance. The pseudo-static loading tests on these specimens were conducted to investigate the effects of influencing factors, such as the axial compression ratio, the thickness of wall (interface contact area), and the addition of a vertical grouted sleeve connection at the horizontal joint, on the seismic performance of PC walls. Analyses and comparisons were conducted in terms of the cracking propagation pattern, failure modes, force-displacement hysteretic curves, skeleton curves, bearing capacity, ductility factors, and energy dissipation of PC walls. It was concluded that the axial compression ratio and adding grouted sleeve connection had a significant influence on the cracking mode of PC walls, whereas the impact of the wall thickness was slight. The shear capacity and energy dissipation capacity of specimen dramatically enhanced by increasing the axial compression ratio or adding grouted sleeve connection. The PC wall exhibits good ductility after adding the vertical grouted sleeve connection at a horizontal joint. However, the ductility factor increases firstly and then decreases in the enhancement of the axial compression ratio. The reduction in wall thickness has remarkable impacts on the shear strength and energy dissipation capacity of specimens, but the influences on ductility were not significant. The prediction method for calculating the shear capacity of PC walls with alveolar-type horizontal joints was proposed based on the experimental data, and these calculated results are in good agreement with the experimental results.

Effect of Solidification and Hot Rolling Processes on Wear Performance of TiC-Reinforced Wear-Resistant Steel.

As a commonly reinforcing phase in wear-resistant materials, TiC is often added into wear-resistant materials to improve the wear resistance. The independently developed stepped molds with variable thicknesses were used to prepare the TiC-reinforced steels with the same composition though melt solidification processing to study the effect of the solidification rate on the particle size and wear performance. The effect of the hot rolling compression ratio on the particle size and wear performance was also studied. The length and aspect ratios of the particles in heat-treated TiC-reinforced steels with different billet thicknesses and rolling compression ratios were measured. With the increasing in the billet thickness and the decreasing in the rolling compression ratio, the length and aspect ratio of the particles increased in heat-treated TiC-reinforced steels, and the hardness decreased slightly. The three-body abrasive wear behavior of the TiC-reinforced steels was conducted using a standard dry sand rubber wheel wear testing procedure, and the modeling of the wear mechanism was established. The particle size is the main factor affecting wear resistance when the hardness of TiC-reinforced steels is similar. When the particles size is moderate, about 2-6 µm, the particle can break the sand tip and hinder the sand tip from sliding on the surface. In this manner, the mass loss decreased and the wear resistance improved. The large particles will be broken easily by the abrasive, and the small particles are removed easily by the abrasive in the wear process. So, the large and small particles cannot effectively prevent the damage of the abrasive to the matrix, and they have less of an effect on improving wear resistance.

Ghost edge detection based on HED network.

In this paper, we present an edge detection scheme based on ghost imaging (GI) with a holistically-nested neural network. The so-called holistically-nested edge detection (HED) network is adopted to combine the fully convolutional neural network (CNN) with deep supervision to learn image edges effectively. Simulated data are used to train the HED network, and the unknown object's edge information is reconstructed from the experimental data. The experiment results show that, when the compression ratio (CR) is 12.5%, this scheme can obtain a high-quality edge information with a sub-Nyquist sampling ratio and has a better performance than those using speckle-shifting GI (SSGI), compressed ghost edge imaging (CGEI) and subpixel-shifted GI (SPSGI). Indeed, the proposed scheme can have a good signal-to-noise ratio performance even if the sub-Nyquist sampling ratio is greater than 5.45%. Since the HED network is trained by numerical simulations before the experiment, this proposed method provides a promising way for achieving edge detection with small measurement times and low time cost.

Automated Vertebral Segmentation and Measurement of Vertebral Compression Ratio Based on Deep Learning in X-Ray Images.

Vertebral compression fracture is a deformity of vertebral bodies found on lateral spine images. To diagnose vertebral compression fracture, accurate measurement of vertebral compression ratio is required. Therefore, rapid and accurate segmentation of vertebra is important for measuring the vertebral compression ratio. In this study, we used 339 data of lateral thoracic and lumbar vertebra images for training and testing a deep learning model for segmentation. The result of segmentation by the model was compared with the manual measurement, which is performed by a specialist. As a result, the average sensitivity of the dataset was 0.937, specificity was 0.995, accuracy was 0.992, and dice similarity coefficient was 0.929, area under the curve of receiver operating characteristic curve was 0.987, and the precision recall curve was 0.916. The result of correlation analysis shows no statistical difference between the manually measured vertebral compression ratio and the vertebral compression ratio using the data segmented by the model in which the correlation coefficient was 0.929. In addition, the Bland-Altman plot shows good equivalence in which VCR values are in the area within average ± 1.96. In conclusion, vertebra segmentation based on deep learning is expected to be helpful for the measurement of vertebral compression ratio.

Research and Development of Self-Contained Water Injection Systems.

Reducing fuel consumption and thus CO2 emissions is one of the most urgent tasks of current research in the field of internal combustion engines. Water Injection has proven its benefits to increase power or optimize fuel consumption of passenger cars. This technology enables knock mitigation to either increase the engine power output or raise the compression ratio and efficiency while enabling λ = 1 operation in the complete engine map to meet future emission targets. Current systems have limited container capacity. It is necessary to refill the water tank regularly. This also means that we cannot get the benefits of an engine with a higher compression ratio. For this reason, the self-contained system was investigated. This article is a methodology for finding the right design of a self-contained water injection system, but also a vehicle test that proves the function.

Diagnostic value of multi-slice spiral CT scan in lung compression ratio of patients with pulmonary contusion complicated by pneumothorax or hydropneumothorax.

OBJECTIVE: This study was designed to explore the diagnostic value of multi-slice spiral CT (MSCT) scanning in lung compression ratio of patients with pulmonary contusion complicated by pneumothorax or hydropneumothorax. METHODS: Seventy-eight patients with pulmonary contusions complicated by pneumothorax or hydropneumothorax treated in the Department of Emergency Surgery of our hospital were examined by CT and X-ray, and the diagnostic value of these two methods was observed. The correlation of lung compression ratio measured by multiplanar reconstruction (MPR) and volume rendering (VR) with W/D ratio was studied, and the formula between VR-measured lung compression ratio and W/D ratio was constructed using a one-variable linear regression equation. RESULTS: The diagnostic rate of pulmonary contusions complicated by pneumothorax or hydropneumothorax measured by CT was higher than that by X-ray (P<0.05). Among the patients with pulmonary contusion diagnosed by CT, 45 were localized and 33 were extensive, and there were statistically significant differences in the incidence of comorbid rib fractures (P<0.05). The correlation of lung compression ratio measured by VR with W/D ratio measured by CT was analyzed, and the regression equation of the two was obtained by one-variable linear regression equation analysis: lung compression ratio =1.159* W/D -1.034. VR-measured lung compression ratio measured was positively correlated with W/D ratio (r=0.936, P<0.001). CONCLUSION: CT is superior to X-ray in the diagnosis of pulmonary contusions complicated by pneumothorax or hydropneumothorax. The calculation of lung compression ratio using the formula of lung compression ratio =1.159* W/D -1.034 has certain clinical value and can improve clinical work efficiency.

Quantification of enamel decussation in gracile and robust capuchins (Cebus, Sapajus, Cebidae, Platyrrhini).

Multiple behavioral and biomechanical analyses have demonstrated that capuchin monkeys (Cebus and Sapajus) are specialized for breaking down hard-object foods as compared to other cebid monkeys. In addition to a complex suite of craniodental adaptations, it has specifically been demonstrated that capuchins possess highly complex dental enamel, with extensive Hunter-Schreger banding and other decussation, that likely serve as an adaptation to resist crack propagation during hard-object feeding. Furthermore, it has been demonstrated that robust capuchins (Sapajus spp., formerly Cebus apella) demonstrate further adaptation for hard-object feeding than other capuchins, routinely breaking down extremely mechanically challenging foods. However, there has been no comparison of dental enamel complexity in robust versus gracile capuchins, to assess whether the dental enamel in Sapajus follows this same pattern of further specialization. Therefore, this study compares dental enamel complexity in images of dental thin sections from a sample of robust versus gracile capuchins using image compression ratio (ICR) analysis. ICR is a variable that correlates with enamel complexity, such that higher ICR values are indicative of increased complexity in the form of enamel decussation. We found no significant difference between robust and gracile capuchins when assessing all teeth in our sample together, however, we did find that robust capuchins have significantly higher ICR values than gracile capuchins for canine teeth, specifically. Our results support prior studies suggesting that robust capuchins are specialized to generate increased masticatory loads with their anterior dentition, specifically, as compared to gracile species.

Exploring the efficiency and pollutant emission of a dual fuel CI engine using biodiesel and producer gas: An optimization approach using response surface methodology.

The present study focuses on optimizing the engine operating parameters of a dual-fuel (DF) engine. Producer gas (PG) and Honge oil methyl ester (HOME) are used as primary fuel and pilot fuel respectively for the operation. An experimental design matrix of 20 different combinations was considered using Design of Experiments (DoE), based on the central composite design (CCD) of response surface methodology (RSM). The effects of these combinations were experimentally investigated to calculate the performance and emission characteristics of the engine. The objective of the work is to maximize the Brake thermal efficiency (BTE) and minimize the exhaust gas temperature (EGT), nitrogen oxide (NOx), hydrocarbon (HC), and carbon monoxide (CO) emissions. The RSM model is developed using the experimental data and further, the operating parameters were optimized using the desirability approach. The optimized combination of operating parameters was obtained at 61.10% engine load, compression ratio (CR) of 18, and injection timing (IT) of 23.30° before top dead center (BTDC). The optimum responses corresponding to these operating conditions were found as 14.23%, 354.29 °C, 52.18 ppm, 39.53 ppm, and 0.51% for BTE, EGT, NOx, HC, and CO respectively with an overall desirability of 0.962. The optimized responses were validated experimentally at optimum input conditions and found to be within acceptable error levels. Further, an economic analysis of the optimized DF system is also carried out.

A Systematic Review of Hardware-Accelerated Compression of Remotely Sensed Hyperspectral Images.

Hyperspectral imaging is an indispensable technology for many remote sensing applications, yet expensive in terms of computing resources. It requires significant processing power and large storage due to the immense size of hyperspectral data, especially in the aftermath of the recent advancements in sensor technology. Issues pertaining to bandwidth limitation also arise when seeking to transfer such data from airborne satellites to ground stations for postprocessing. This is particularly crucial for small satellite applications where the platform is confined to limited power, weight, and storage capacity. The availability of onboard data compression would help alleviate the impact of these issues while preserving the information contained in the hyperspectral image. We present herein a systematic review of hardware-accelerated compression of hyperspectral images targeting remote sensing applications. We reviewed a total of 101 papers published from 2000 to 2021. We present a comparative performance analysis of the synthesized results with an emphasis on metrics like power requirement, throughput, and compression ratio. Furthermore, we rank the best algorithms based on efficiency and elaborate on the major factors impacting the performance of hardware-accelerated compression. We conclude by highlighting some of the research gaps in the literature and recommend potential areas of future research.

Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case.

The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.