Adjacent Angles Research Articles

Locomotion and Postural Control in Young Adults with Autism Spectrum Disorders: A Novel Kinesiological Assessment.

Background/Objectives: The purposes of the present study were to assess gait by using a novel approach that plots two adjacent joint angles and the postural control in individuals with autism (ASD) and individuals with typical neurodevelopmental (TD). Methods: The surface electromyography (sEMG) activity was measured synchronously with the other variables. Twenty young adult men, 10 with TD and 10 with a diagnosis of ASD, took part in this study. Results: There was a significant difference between ASD and TD groups in the area described by the knee-ankle diagram (p < 0.05). The sEMG activity recorded from the lateral gastrocnemius (LG) during the contact phase of gait was significantly lower in the ASD group compared with the TD group (p < 0.05). The sEMG activity recorded in the different postural conditions showed differences in LG and tibialis anterior (TA) between the ASD and TD groups (p < 0.05). Conclusions: The knee-ankle diagram provided a sensitive and specific movement descriptor to differentiate individuals with ASD from individuals with TD. The reduced LG activation is responsible for the reduced area in the knee-ankle diagram and 'toe-walking' in individuals with ASD and represents the common denominator of an altered ankle strategy during locomotion and postural control.

Analysis of factors affecting bone volume changes after immediate implantation in the maxillary central incisor.

This study aimed to evaluate the clinical outcomes of immediate implantation of single maxillary central incisor and explore factors affecting post-implant bone volume. Clinical data and imaging records from pre-surgery, the day of surgery, and 6 months post-surgery of 100 patients (100 implants) with non-salvageable maxillary central incisors who underwent immediate implantation were collected. Bone thickness at the cervical, middle, and apical regions of the implant's labial and palatal sides were measured immediately post-surgery and at 6 months, and bone volume changes were observed. A regression analysis model was used to assess predictive factors for labial and palatal bone plate thickness. At 6 months post-surgery, the labial bone thicknesses at the cervical, middle, and apical regions were 2.35, 2.29, and 3.28 mm, respectively, and those of the palatal side were 0.00, 2.40, and 6.05 mm, respectively. The cervical region had the highest alveolar crest collapse rates, with 32.87% on the labial side and 62.20% on the palatal side. The regression model indicated that factors influencing the thickness of bone at the cervical labial side of the implant included initial bone thickness, the implant center to adjacent tooth center angle, implant diameter, and the type of implant closure (P<0.05). The initial bone thickness on the palatal side was the sole predictor for bone thickness on the palatal side (P<0.05). Immediate implantation of single maxillary central incisors yields effective clinical results. The thickness of new bone around the implant is influenced by multiple factors. A comprehensive consideration of these factors in the planning of immediate implantation is necessary to achieve optimal therapeutic outcomes.

High-accuracy direction measurement and high-resolution computational spectral reconstruction based on photonic crystal array

Portable and wearable miniaturized spectrometers play a crucial role in various fields. In this paper, we present a method for simultaneously realizing high-accuracy direction measurement and high-resolution computational spectral reconstruction based on the angle sensitivity of conventional photonic crystals (PCs), wherein an optical filter array is composed of multiple one-dimensional PCs. The high-angle sensitivity of PCs results in angle-dependent optical spectra. When these spectra with different angles are used to reconstruct the target spectra in an unknown direction and the interval between adjacent angles is sufficiently small, the accurate direction of the target can be automatically identified. Moreover, the computational spectra still have high resolution over a wide range of incidences. The computational spectra under arbitrary polarizations can also be recognized based on the polarization dependence of the PCs at an oblique incidence. Our research results are significant for engineering a new miniaturized comprehensive computational spectrometer with target-direction perception and omnidirectional spectral reconstruction abilities.

Interaction of short-crested waves with cylinder and concentric segmented arc breakwaters

Using the outer breakwater of Palm Jumeirah in Dubai as a physical geometric model, the diffraction problem of short-crested waves interacting with concentric segmented arc structures was theoretically investigated using linear water wave theory. In this study, the watershed was partitioned into two regions, and a unique coordinate system was established to describe the velocity potential function within each region. The interface between the two regions connects the velocity potentials across them using the matching eigenfunction expansion technique. By accounting for the boundary conditions, the integral equation was streamlined into a series of algebraic equations, which were subsequently resolved to determine an unidentified function. The precision of the model was validated through a comparison with findings from the literature. Numerical investigations have elucidated the correlation between changes in wave force, cylinder run-up, and parameters such as the spacing between adjacent arcs, opening angle, and porous coefficient. The numerical results indicated that the impermeable segmented arcs structure provides better protection against short-crested and plane waves, whereas the permeable segmented arc structure provides better protection against standing waves. Interestingly, for a segmented three-arc structure, when the segments are moderately spaced, the protection of the interior region is superior to that of an unsegmented arc structure.

Identification of force chains in wet coal dust layer and the effect of porosity on three-body contact stiffness

Aiming at the three-body contact problem of mechanical rough surface containing wet coal dust interface, the three-body contact model of rough surface containing wet coal dust interface is constructed by comprehensively considering the contact deformation of rough surface and contact characteristics of wet coal dust, and based on the crushing theory. By analysing the contact force, load-bearing particle size and adjacent contact angle thresholds of the wet coal dust layer, the force chain identification criterion is formulated. Finally, quantitative calculations of the force chain characteristics are performed to reveal the effect of different initial porosities on the three-body contact stiffness, which is verified experimentally. The results of the study show that the average contact force of the wet coal dust layer can be used as the force chain contact force threshold, the average particle size can be used as the force chain particle size threshold, and the force chain angle threshold is determined by the particle coordination number. As the initial porosity decreases, the number, length and stiffness of force chains in the wet coal dust layer increase significantly, and the stiffness reaches a maximum value of 2.007 × 108 pa/m at the moment of downward pressure to stabilisation, while the trend of force chain bending varies in the opposite direction, and its minimum bending degree decreases to 20°. The maximum relative error between the simulation and experimental results of three-body contact stiffness is 9.64%, which proves the accuracy of the force chain identification criterion and the quantitative calculation of three-body contact stiffness by force chain.

Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency.

Exploring Children's representations of work: A review investigating content and influences

Middle childhood has been identified as a critical period regarding the exploration and construction of the self, with strong implications for future vocational choices and occupational trajectories. Due to a shortage of both theoretical models and empirical data, a knowledge gap remains as regards children's perceptions and understandings of the concept of work between the ages of 5–8, and the differential variables influencing these representations. This review aims to fill this gap by providing relevant information with respect to the investigation of the content of children's representations of work, as well as the factors influencing them. Considering the lack of papers covering this topic, this article approaches the subject through adjacent angles such as adult and adolescent representations of work, children's representations of occupations, and children's vocational preferences or career development. A theoretical model of children's mental representations of work is presented, and general methodological avenues are proposed to pursue further investigation on this research topic.

Parametric solutions to the kinematics of developable degree-4 rigid origami vertices

Developable degree-4 (DD4) vertices have four facets and four creases and can be unfolded flat. The rigid-folding kinematics of DD4 vertices is rich in that it generally has two folding modes and can get stuck when two facets bind together. To study the full spectrum of the kinematics of DD4 vertices, parametric solutions for fold angles in terms of the cotangents of half-angles are derived from the opposite and adjacent fold angle relationships. It is shown that any two fold angles of a general DD4 vertex are related by the equation of a hyperbola. When the vertex has collinear creases or is flat-foldable, the pertinent hyperbola equations degenerate into linear relationships. Meanwhile, when DD4 vertices are classified into three categories according to Grashof’s criterion, both unique and binding folds can be readily located from the facet with the largest or smallest sector angle. The rigid-folding kinematics of typical vertices is then investigated. In addition to the flat state, the two folding modes can also be switched at the binding states if self-intersection is permitted. The results provide new formulae and clear geometric views on the rigid-folding kinematics of DD4 vertices, which are fundamental for constructing larger origami patterns.

Adjacent angle size correlates with diagnostic sensitivity of endobronchial ultrasonography with a guide sheath

Adjacent angle size correlates with diagnostic sensitivity of endobronchial ultrasonography with a guide sheath

Early Compensatory Segmental Angle Changes at L3-L4 and L4-L5 After a L5-S1 Interbody Fusion for a Grade 1 Spondylolisthesis.

The retrospective study included patients who underwent an L5-S1 anterior (ALIF) or transforaminal (TLIF) lumbar interbody fusion with posterior pedicle screw instrumentation for grade 1 spondylolisthesis from 2018 to 2022. To compare early reciprocal changes at the L3-L4 and L4-L5 adjacent levels 6 months after ALIF or TLIF at L5-S1. Degenerative and chronic isthmic spondylolistheses often result in decreased segmental lordosis (SL) at L5-S1. This can lead to lordotic overcompensation at adjacent levels to maintain spinopelvic balance. However, the fate of adjacent angles after interbody fusion is not well understood. Preoperative and 6-month postoperative measurements of SL (L3-L4, L4-L5, and L5-S1), lumbar lordosis, and pelvic incidence (PI) were obtained from sagittal standing radiographs. Preliminary t tests were performed for descriptive purposes, and multiple regression was used for hypothesis testing. Ninety-eight patients met the inclusion criteria (50 ALIF and 48 TLIF). A greater amount of lordosis achieved at L5-S1 was significantly associated with a greater reduction of SL at L4-L5 ( r = -0.65, P < 0.001) or L3-L4 ( r = -0.46, P < 0.001). A greater preoperative PI was associated with a greater reduction of SL at L4-L5 ( r = -0.42, P < 0.001) and at L3-L4 ( r = -0.44, P < 0.001). At 6 months after a lumbar interbody fusion at L5-S1, greater compensatory changes with lordosis reduction are observed at the supra-adjacent L4-L5 and L3-L4 levels in patients achieving greater L5-S1 SL. In addition, preoperative PI played a role in influencing lordotic correction.

Automated measurements of interscrew angles in vertebral body tethering patients with deep learning

BACKGROUND CONTEXTVertebral body tethering is the most popular nonfusion treatment for adolescent idiopathic scoliosis. The effect of the tether cord on the spine can be segmentally assessed by comparing the angle between two adjacent screws (interscrew angle) over time. Tether breakage has historically been assessed radiographically by a change in adjacent interscrew angle by greater than 5° between two sets of imaging. A threshold for growth modulation has not yet been established in the literature. These angle measurements are time consuming and prone to interobserver variability. PURPOSEThe purpose of this study was to develop an automated deep learning algorithm for measuring the interscrew angle following VBT surgery. STUDY DESIGN/SETTINGSingle institution analysis of medical images. PATIENT SAMPLEWe analyzed 229 standing or bending AP or PA radiographs from 100 patients who had undergone VBT at our institution. OUTCOME MEASURESPhysiologic Measures: An image processing algorithm was used to measure interscrew angles. METHODSA total of 229 standing or bending AP or PA radiographs from 100 VBT patients with vertebral body tethers were identified. Vertebral body screws were segmented by hand for all images and interscrew angles measured manually for 60 of the included images. A U-Net deep learning model was developed to automatically segment the vertebral body screws. Screw label maps were used to develop and tune an image processing algorithm which measures interscrew angles. Finally, the completed model and algorithm pipeline was tested on a 30-image test set. Dice score and absolute error were used to measure performance. RESULTSInter- and Intra-rater reliability for manual angle measurements were assessed with ICC and were both 0.99. The segmentation model Dice score against manually segmented ground truth across the 30-image test set was 0.96. The average interscrew angle absolute error between the algorithm and manually measured ground truth was 0.66° and ranged from 0° to 2.67° in non-overlapping screws (N=206). The primary modes of failure for the model were overlapping screws on a right thoracic/left lumbar construct with two screws in one vertebra and overexposed images. An algorithm step which determines whether an overlapping screw was present correctly identified all overlapping screws, with no false positives. CONCLUSIONWe developed and validated an algorithm which measures interscrew angles for radiographs of vertebral body tether patients with an accuracy of within 1° for the majority of interscrew angles. The algorithm can process five images per second on a standard computer, leading to substantial time savings. This algorithm may be used for rapid processing of large radiographic databases of tether patients and could enable more rigorous definitions of growth modulation and cord breakage to be established.

A Comparison of Corpectomy ACDF Hybrid Procedures with Nano-Hydroxyapatite/Polyamide 66 Cage and Titanium Mesh Cage for Multi-level Degenerative Cervical Myelopathy: A Stepwise Propensity Score Matching Analysis.

Previous studies have found satisfactory clinical results with the nano-hydroxyapatite/polyamide 66 (n-HA/PA66) cage to reconstruct the stability of anterior cervical column. However, studies evaluating the long-term outcomes of the n-HA/PA66 cage in multi-level degenerative cervical myelopathy (MDCM) have not been reported. This study aims to compare the outcomes of corpectomy anterior cervical discectomy and fusion (ACDF) hybrid procedures between the n-HA/PA66 cage and titanium mesh cage (TMC) to treat MDCM. After the screening for eligibility, this retrospective study involved 90 patients who underwent corpectomy ACDF hybrid (CACDFH) procedure from June 2013 to June 2018. The CACDFH procedure is the combination of ACDF and anterior cervical corpectomy and fusion (ACCF). According to the cage utilized, we categorized patients into a n-HA/PA66 cage group and a TMC group. Then, stepwise propensity score matching (PSM) was performed to maintain comparable clinical data between groups. All the patients were followed up ≥4 years and the longest follow-up time was 65.43 (±11.49) months. Cage subsidence, adjacent segment degeneration (ASD), segmental height (SH), segmental angle (SA), cervical lordosis (CL), and clinical data (visual analogue scale [VAS] and Japanese Orthopaedic Association [JOA] score) was evaluated preoperatively, at 1 week, and at the final surgery follow-up. The independent student's t test and chi-square test were applied to compare the differences between groups. Through PSM analysis, 25 patients from the n-HA/PA66 group were matched to 25 patients in the TMC group. The occurrence of ASD was 16.0% (4/25) in the n-HA/PA 66 group, which was significantly less than in the TMC group at 44.0% (11/25) (p = 0.031). Moreover, the cage subsidence rate was significantly higher in the TMC group as compared to the n-HA/PA 66 group (40.0% vs. 12.0%, p = 0.024). But there was no significant difference in SH, SA, and CL at any time after surgery as determined through follow-up. The VAS and JOA scores significantly improved in both groups at 3 months postoperative and at final follow-up. However, there were no significant differences in the VAS and JOA score at any time between the two groups in preoperative (p > 0.05). The n-HA/PA66 cage is associated with lower rate of cage subsidence and ASD than the TMC in the treatment of MDCM. The n-HA/PA66 cage could be superior to the TMC in corpectomy ACDF hybrid procedures.

Optimizing welding sequence of TIG cross-joint of Invar steel using residual stresses and deformations

In this paper, a number of welding sequences were designed by numerical simulation to study the welding deformation of Invar steel cross-splicing joint during diagonal welding and adjacent angle welding, and the optimal welding deformation control process was obtained. Results show that segmental welding can control effectively welding deformation. Material on both sides of the weld was under tensile stresses and became compressed along the thickness direction during welding. When segmented welding is studied, irrespective of the welding sequence used in the upper and lower half welds, it is found that it had strong effect on welding deformation control of the joint. When the welding sequence of the upper and lower half welds is opposite, the welding deformation is minimum. When welding a series of welds in an inwards direction from the outside to the inside for large cross-splicing structures, the joint welding deformation is symmetrical, which has the best control effect on the overall joint deformation, but the deformation at the four corners of the large cross-splicing structure is still significant.

A fast tomosynthesis method for printed circuit boards based on a multiple multi-resolution reconstruction algorithm.

Digital tomosynthesis (DTS) technology has attracted much attention in the field of nondestructive testing of printed circuit boards (PCB) due to its high resolution and suitability to thin slab objects. However, the traditional DTS iterative algorithm is computationally demanding, and its real-time processing of high-resolution and large volume reconstruction is infeasible. To address this issue, we in this study propose a multiple multi-resolution algorithm, including two multi-resolution strategies: volume domain multi-resolution and projection domain multi-resolution. The first multi-resolution scheme employs a LeNet-based classification network to divide the roughly reconstructed low-resolution volume into two sub-volumes namely, (1) the region of interest (ROI) with welding layers that necessitates high-resolution reconstruction, and (2) the remaining volume with unimportant information which can be reconstructed in low-resolution. When X-rays in adjacent projection angles pass through many identical voxels, information redundancy is prevalent between the adjacent image projections. Therefore, the second multi-resolution scheme divides the projections into non-overlapping subsets, using only one subset for each iteration. The proposed algorithm is evaluated using both the simulated and real image data. The results demonstrate that the proposed algorithm is approximately 6.5 times faster than the full-resolution DTS iterative reconstruction algorithm without compromising image reconstruction quality.

Gamma error correction algorithm for phase shift profilometry based on polar angle average

Phase errors caused by the gamma nonlinear response of the phase shift profilometry (PSP) severely affect 3D measurement accuracy. To tackle this, a simple phase error compensation technique based on polar angle average is presented in this paper to improve the accuracy. Wrapped phase values are regarded as polar angles, and a polar axis distribution map can be obtained in the polar coordinate. Practically, the polar axis distribution (PAD) of the undistorted wrapped phase is uniform. When there are nonlinear effects in an PSP, the polar axis is unevenly distributed. The difference between adjacent polar angles is computed and then rearranged with specifically labels. After that, the even PAD diagram is generated, and the smooth phase can be further recovered. Compared with conventional nonlinearity correction methods, the proposed method corrects the error without any auxiliary conditions. Its effectiveness and robustness are verified in simulations and experiments.

Lumbar scoliosis and stenosis: What outcomes for which treatment? Analysis of three surgical techniques in 154 patients with minimum two-year follow-up

Study designProspective multicentric study. ObjectiveThis study goal was to analyze the clinical and radiographic outcomes of lumbar stenosis and scoliosis (LSS) patients, treated with lumbar decompression (LD), short fusion and decompression (SF) or long fusion with deformity correction (LF). HypothesisProcedures without correction lead to poorer long-term outcomes. MethodsConsecutive patients with two-year minimum follow-up, older than 50, with lumbar scoliosis (Cobb angle>15°), and symptomatic lumbar stenosis were included. Age, gender, Lumbar and Radicular Visual Analog Scale, ODI, SF12 and SRS30 were collected. Main and adjacent curves Cobb angles, C7 coronal tilt (C7CT), spinopelvic parameters, and spino-sacral angle (SSA) were measured preoperatively, at one and two years. Patients were sorted into surgery type groups. ResultsIn total, 154 patients were included, with respectively 18, 58 and 78 patients in LD, SF and LF groups. Mean age was 69, 85% were women. Clinical scores improved in each group at one year, but only LF group exhibited persistent improvement at 2years. A significant fractional Cobb angle increase was noted in the SF group at 2years (from 12±11° to 18±14°). C7CT significantly increased in the LD group at 2years (from 2.5±1.3° to 5.1±3.5°). LF group presented the highest complication rate (45%, 19% for SF and 0% for LD). The overall revision rate was 14% in SF group and 30% in LF group. ConclusionLSS is a complex pathology requiring custom-made surgical treatment. LD, SF and LF allow satisfactory clinical outcome, with a better and more sustained clinical improvement for LF despite higher complication and revision rates. Level of evidenceIV.

Early cement augmentation may be a good treatment option for pain relief for osteoporotic compression fractures: a systematic review and meta-analysis.

The incidence of osteoporotic compression fractures (VCFs) have been rising over the past decades. Presently, vertebral cement augmentation procedures such as balloon kyphoplasty and vertebroplasty are common treatments allowing pain relief and functional recovery. However, there is controversy on whether different timeframes for cement augmentation affects clinical outcomes. Hence, this study aimed to compare pain relief and complication rates between early versus late cement augmentation. A comprehensive systematic review of PubMed, EMBASE, Scopus and Cochrane Library was conducted, identifying studies that compared early versus late cement augmentation for VCFs. As the definitions of "early" and "late" phases across studies are heterogenous, we established the cut-off between early and late phase as intervals to accommodate as many studies as possible for analysis. We conducted two separate analyses with different cut-off intervals and included studies that reported interventions within these respective time intervals. In analysis 1, we included studies which grouped patients into "early" and "late" group based on a cut-off time frame of 2-4weeks. On the other hand, in analysis 2, we included studies which grouped patients into "early" and "late" groups based on a cut-off time frame of 6-8weeks. Meta-analysis was conducted via random-effect models, comparing outcomes of interest between early and late groups. Eleven studies were included. The total cohort size was 712 and 775 patients in analysis 1 and 2 respectively. Mean follow-up was 12.9 ± 3.7months and 11 ± 0.6months respectively. VAS change at final follow-up was significantly greater in the early group for both analyses. (MD = - 0.66, p = 0.01; and MD = - 1.18, p < 0.005 respectively). There was no significant difference in post-operative absolute VAS score, number of cement leakage, number of adjacent compression fractures and local kyphotic angle, for both analyses. Patients in both groups experienced reductions in VAS score that exceeded the minimum clinically important difference. Both early and late timeframes for cement augmentation offered significant improvement in pain relief, with similar post-operative absolute pain score, kyphotic angle, cement leakage and adjacent vertebral fractures. Early surgery may offer substantial pain relief in patients presenting with pain as early as < 2-4weeks of VCFs.

What is the fate of the adjacent segmental angles 6 months after single-level L3–4 or L4–5 lateral lumbar interbody fusion?

Background ContextLateral lumbar interbody fusion (LLIF) is an effective technique for fusion and sagittal alignment correction/maintenance. Studies have investigated the impact on the segmental angle and lumbar lordosis (and pelvic incidence-lumbar lordosis mismatch), however not much is documented regarding the immediate compensation of the adjacent angles. PurposeTo evaluate acute adjacent and segmental angle as well as lumbar lordosis changes in patients undergoing a L3–4 or L4–5 LLIF for degenerative pathology. Study Design/SettingRetrospective cohort study. Patient SamplePatients included in this study were analyzed pre- and post-LLIF performed by one of three fellowship-trained spine surgeons, 6 months following surgery. Outcome MeasuresPatient demographics (including body mass index, diabetes diagnosis, age, and sex) as well as VAS and ODI scores were measured. Lateral lumbar radiograph parameters: lumbar lordosis (LL), segmental lordosis (SL), infra and supra-adjacent segmental angle, and pelvic incidence (PI). MethodsMultiple regressions were applied for the main hypothesis tests. We examined any interactive effects at each operative level and used the 95% confidence intervals to determine significance: a confidence interval excluding zero indicates a significant effect. ResultsWe identified 84 patients who underwent a single level LLIF (61 at L4–5, 23 at L3–4). For both the overall sample and at each operative level, the operative segmental angle was significantly more lordotic postop compared to preop (all ps≤.01). Adjacent segmental angles were significantly less lordotic postop compared to pre-op overall (p=.001). For the overall sample, greater lordotic change at the operative segment led to more compensatory reduction of lordosis at the supra-adjacent segment. At L4–5, more lordotic change at the operative segment led to more compensatory lordosis reduction at the infra-adjacent segment. ConclusionThe present study demonstrated that LLIF resulted in significant increase in operative level lordosis and a compensatory decrease in supra- and infra-adjacent level lordosis, and subsequently no significant impact on spinopelvic mismatch.

Transient Flow Performance of a Vertical Well With Multiple Varying Conductivity Fractures in a Tight Oil Reservoir

Summary Due to uneven proppant distribution and varied proppant sizes during hydraulic fracturing, artificial fractures of varying length, asymmetry, and varying conductivity are easily formed near the wellbore. The principal focus of this work is to investigate the pressure transient performance of a vertical well penetrated by multiple asymmetrical fractures with varying lengths and varying conductivities in a tight oil reservoir. A novel fracture flow equation was developed specifically to describe the flow behavior inside the complex artificial fractures mentioned above. By combining with the point source solution of the tight oil reservoir, a semianalytical solution was further obtained to analyze the pressure transient behavior of a vertical well with multiple varying-conductivity fractures in a tight oil reservoir. The accuracy and reliability of the newly-developed solution were verified by comparing with the result of a numerical model. With this new solution, fracture flux distribution for different conductivity modes, namely, linearly declining mode, exponentially declining mode, and elliptically declining mode, shows that the near-wellbore fracture flux of the exponential mode is greater than that of the other two modes, but the flux distribution near the fracture tips is on the contrary. Meanwhile, the transient flow characteristics under the above varying conductivity modes indicate that the exponentially varying conductivity has a significant influence on the early linear flow regimes, while the linear and elliptical mode only has a slight influence on the bilinear flow regime under high conductivity. Parameter sensitivity analysis reveals that the obvious inversion point occurring in the pressure derivative curves of uniform conductivity fractures disappears on the pressure derivative curves of varying conductivity fractures, and a weaker asymmetry, a greater adjacent fracture angle, and a larger fracture number and fracture length ratio are conducive to improve the fracturing stimulation effect. This study deepens our understanding of the transient flow performance of vertically fractured wells and helps to estimate artificial fracture properties and evaluate hydraulic fracturing performance.

On the Mastery of Elementary Geometric Concepts¤.

We publish here the report by N.F. Talyzina to a Conference on Psychology in 1955 and released two years later in the proceedings of that conference (N.F. Talyzina [1957]. In B.G. Anan′yeva et al. [Eds.], Materialy soveshchaniia po psikhologii. July 1–6, 1955. Moscow: Publishing House of the Academy of Pedagogical Sciences of the RSFSR.) This report is of particular interest, since it describes some of the first formative experiments based on the theory of planned stage-by-stage formation of mental actions; the text does not yet discuss the formation of actions, but only the application of the attributes of concepts to solving problems. The text presents the results of a study of the formation of elementary geometric concepts according to the theory of planned stage-by-stage formation of mental actions and concepts. Twenty-two subjects from grades 6–9 formed geometric concepts such as “line,” “angle,” “angle bisector,” “perpendicular,” “adjacent angles,” and “supplementary angles.” These attributes were formed in the process of their application to solving different types of problems. Observational and then formative (training) experiments were performed individually. The article contains excerpts from the subjects’ protocols as they solved the problems. It was shown that stage-by-stage development (identifying attributes from a definition, saying them aloud, and then applying them to solving problems) leads to mastery not only of the geometric concepts themselves, but also of the method of action with definitions in general, allowing students to transfer the method they have learned to concepts from another field of knowledge.