在过去20多年里，斜坡地貌学中定量和数学研究的“爆发”显得尤为突出，引发了激烈的争论和讨论。所有这些争论都围绕一个问题：数学在地貌学中能带来什么？支持和反对的意见都有很多，但没有形成共识。如今争论已平息，是时候冷静思考在地貌学中使用数学方法的利弊了。没有必要列举所有使用这些方法的著作——它们数量众多且各不相同。使用这些方法的一大缺点在于缺乏共同的思想和总体框架，无法将各项研究整合成严密的科学理论。其建立因一个情况而受阻。上述“爆发”一方面吸引了大量研究者关注这一问题，另一方面却导致斜坡地貌学中方法和研究成果的范围如此广泛，以至于无论在理论上还是实践上都无法统一到一个方向。因此，大量事实并未导致统一理论的形成。这种情况本身令人沮丧，但积极的一面是，从这种丰富性中明显可以识别出一些工作，对其系统化可能推动地貌学统一理论的进一步发展——该理论基于对理论命题、实验数据和野外观察的实质性分析。\n在过去的10至15年中，我们创建并发表了大量描述不同类型斜坡、斜坡形成过程及其他地形形态发展的数学模型。为此使用了各种数学工具。问题在于，并非所有数学方法都能真正用于描述特定类型斜坡及其过程的发展。事实证明，每种斜坡类型都允许用特定的数学方法描述其发展。因此我们产生了创建一个统一的斜坡发展描述理论的想法，其中每种初始类型都对应其自身的斜坡系统模型圈。我们的研究经验表明，在斜坡地貌学中，应区分出确定性平衡模型发展的一般理论（分别针对一维（平面）和二维（空间）问题），以及一个基于动力系统定性理论的、我们创建的斜坡系统动力模型新领域。这些模型描述了斜坡系统中各要素与作用因素之间的相互作用过程。相互作用问题在地貌学中普遍存在，而斜坡系统中要素的相互作用问题在描述斜坡发展时具有决定性作用。与平衡模型概念不同，动力模型不直接给出斜坡剖面及其空间形态的发展，而是研究过程的物理本质，构建发展理论。因此，地形动力平衡理论由动力模型概念来描述。此外，还存在一类描述边界条件的问题，需要设定这些条件以便针对特定斜坡类型求解。\n本书第三部分描述斜坡过程可能显得有些奇怪——这些过程似乎应该先于形态描述。其实，按照我们的构想，这一部分应是数学方法在斜坡地貌学中实际应用的示例。由于当前的应用是选择性的，因此第三部分也具有片段性。在前两部分中，斜坡既作为封闭系统也作为开放系统加以考察，但后续将引入边界上的建模（例如与水文系统等的边界）。由于篇幅有限，边界问题的求解方法仅在非标准情况下给出。\n作者衷心感谢西蒙诺夫 Д. Г.教授、博尔苏克 О. А.副教授、莫斯科大学地貌学教研室数学建模实验室主任泽伊迪斯 И. М.在审阅本书手稿时提出的宝贵意见和建议，以及责任编辑斯图皮申 А. В.教授。\n
", "ds_source": "作者（编委会）：А.М. 特罗菲莫夫， В.М. 莫斯科夫金 (А.М.Трофимов, В.М.Московкин)\n出版社：Издательство Казанского университета\n出版地：莫斯科\n出版年：1983年\n页数：216页 \n语种：俄文\n馆藏条形码：XJLAS RU 70019458\n
", "ds_process_way": "本书为中国科学院新疆生态与地理研究所文献信息中心（以下简称中心）馆藏文献，中心将本书电子化后存储，已经过OCR识别，数据加工过程依据国家标准《GB/T 31219.2-2014图书馆馆藏资源数字化加工规范》，完全遵照《斜坡地貌学中的数学建模》的数据信息，未改动删减。\n
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", "ds_acq_start_time": "2025-07-01 00:00:00", "ds_acq_end_time": "2025-07-01 00:00:00", "ds_acq_place": "苏联", "ds_acq_lon_east": null, "ds_acq_lat_south": null, "ds_acq_lon_west": null, "ds_acq_lat_north": null, "ds_acq_alt_low": null, "ds_acq_alt_high": null, "ds_share_type": "apply-access", "ds_total_size": 29038838, "ds_files_count": 1, "ds_format": "PDF格式", "ds_space_res": "无", "ds_time_res": "无", "ds_coordinate": "无", "ds_projection": "无", "ds_thumbnail": "5bdf647f-dcae-4651-8245-c4f4ecef60bb.jpg", "ds_thumb_from": 0, "ds_ref_way": "", "paper_ref_way": "", "ds_ref_instruction": "", "ds_from_station": null, "organization_id": "a5877b42-96ea-4f13-af7e-246f355413d6", "doi_value": "", "subject_codes": [ "170.45" ], "quality_level": 1, "publish_time": "2026-09-18 16:55:45", "first_publish_time": null, "last_updated": "2026-09-18 16:55:45", "protected": false, "protected_to": null, "lang": "zh", "cstr": "33110.11.ariddc.01786", "license": null, "extra": null, "files_shape": [ { "name": "20250701002(XJLASRU70002256).pdf", "size": 29038838, "is_dir": false } ], "features": null, "data_level": 0, "i18n": { "en": { "title": "", "ds_abstract": "Over the past two decades, the “explosion” of quantitative and mathematical research in slope geomorphology has been particularly striking, giving rise to intense debate and discussion. All of these debates revolved around a single question: What can mathematics contribute to geomorphology? Numerous arguments were advanced both in support of and against its application, yet no consensus emerged. Now that the controversy has largely subsided, the time has come to reflect calmly on the advantages and disadvantages of using mathematical methods in geomorphology. There is no need to enumerate all the studies that have employed such methods, as they are both numerous and highly diverse. One major drawback of these approaches is the absence of a common conceptual basis and an overarching framework capable of integrating individual studies into a rigorous scientific theory. The formation of such a theory has been hindered by a particular circumstance. On the one hand, the aforementioned “explosion” attracted the attention of a large number of researchers; on the other hand, it led to such diversity in methods and research results within slope geomorphology that they could not be unified into a single direction, either theoretically or practically. Consequently, the accumulation of facts did not result in the creation of a unified theory. Although this situation is discouraging in itself, its positive aspect is that, within this diversity, one can clearly identify a number of studies whose systematization may contribute to the further development of a unified theory of geomorphology, a theory grounded in the substantive analysis of theoretical propositions, experimental data, and field observations.\r\n\r\nDuring the past ten to fifteen years, we have developed and published a large number of mathematical models describing different types of slopes, slope-forming processes, and the development of other landforms. A wide variety of mathematical tools have been employed for this purpose. The problem is that not all mathematical methods are truly suitable for describing the development of particular types of slopes and their associated processes. It has become evident that each type of slope can be described only through specific mathematical approaches appropriate to its development. This led us to propose the idea of a unified theory for describing slope evolution, in which each initial slope type corresponds to its own family of slope-system models. Our research experience indicates that, in slope geomorphology, it is necessary to distinguish between a general theory of deterministic equilibrium models (developed separately for one-dimensional, or planar, and two-dimensional, or spatial, problems) and a new field that we have established: dynamic models of slope systems based on the qualitative theory of dynamical systems. These models describe the processes of interaction among the various elements of slope systems and the factors acting upon them. The problem of interaction is ubiquitous in geomorphology, and the interaction among components of a slope system plays a decisive role in describing slope development. Unlike equilibrium-model concepts, dynamic models do not directly describe the evolution of slope profiles and their spatial forms; rather, they investigate the physical essence of the processes involved and construct a theory of development. Thus, the theory of geomorphic dynamic equilibrium is represented through the concept of dynamic models. In addition, there exists a class of problems concerned with boundary conditions, which must be specified in order to solve problems related to particular types of slopes.\r\n\r\nThe third part of this book, devoted to slope processes, may appear somewhat unusual, as these processes might seem to precede the description of landforms themselves. In fact, according to our conception, this section is intended to serve as an illustration of the practical application of mathematical methods in slope geomorphology. Since current applications remain selective, the third part is necessarily fragmentary in character as well. In the first two parts, slopes are considered both as closed systems and as open systems; subsequently, however, boundary modeling will be introduced, including boundaries associated with hydrological systems and other related systems. Owing to limitations of space, methods for solving boundary-value problems are presented only for non-standard cases.\r\n\r\nThe author expresses sincere gratitude to Professor D. G. Simonov, Associate Professor O. A. Bolsuk, and I. M. Zeidis, Head of the Mathematical Modeling Laboratory of the Department of Geomorphology at Moscow University, for their valuable comments and suggestions during the review of this manuscript. The author also extends heartfelt thanks to Professor A. V. Stupishin, the scientific editor of this volume.", "ds_source": "Author (Editorial Board): А.М. Trofimov, B.М. Moscow Vkin (А.М.Трофимов, В.М.Московкин)\r\nPublished by: да т ельс т в о к а н с к ого ун и в ерс и т е т а\r\nPublished: Moscow\r\nPublication year: 1983\r\nPages: 216 pages \r\nLanguage: Russian\r\nCollection barcode: XJLAS RU 70019458\r\n
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