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Hi.

1. Is this a case of an elided phrase. "that is," at work?

Use this punctuation mark after a prefix (that is??) followed by a proper noun.

2. I think the part in commas could be made restrictive with the elided phrase "that are." Do you agree? Why do you think it is made a dependent participle phrase (if I termed it correctly)?

These products, invented by John Doe, were designed to help people do this better.
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1-- Yes
2-- As it stands, it is a non-restrictive, nonfinite clause. The author used it because it is extra information about the products, which s/he wished to subordinate. 'That are' would not work; you could use 'that were', but a restrictive clause sounds odd, since the products are already identified earlier in context (this fact is clear from the use of the demonstrative 'these').
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Hi. Thank you.

I wrote this sentence:

These products, invented by John Doe, were designed to help people do this better.

I think I am confused about retaining the present tense for the "eternal truth" aspect of a piece of information. I think these phrases "is invented by" and "was invented by" are used in writing and believe, in both instances, it is assumed that what is invented is in the past, that is, the invention took place in the past. Then, why do you think "is invented by" is used in writing (if I am not mistaken)?

Could we say these?

The XXX which is invented by John Doe is widely used today.

The XXX which is (should be "was"? why?) invented by John Doe was designed to help people lead a better lifestyle.
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'Was', not 'is'. The process of invention is clearly in the past. I suspect that any instances you find of the present tense are non-native or disreputable sources. Please supply any if you find them and I will review them.
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Hi. These are what came up when I did a Google Book Search of the phrase "which is invented by." Can you comment on some? Thank you.

History of the Reformation of the sixteenth century. A new tr. by H. Beveridge‎ - 10 페이지

저자: Jean Henri Merle d'Aubigné - 1845
By the religion of the priest, I mean that which is invented by the priest for
the glory of the priest, and is ruled over by a sacerdotal caste. ...전체보기 - 도서 정보 - 내 서재에 추가하기

The Faith of Catholics: Confirmed by Scripture and Attested by the Fathers ...‎ - 107 페이지

저자: Joseph Berington, John Kirk, James Waterworth, Thomas John Capel - 1884
What is the depositum ? that is that which is committed to thee, not that which
is invented by thee ; what thou hast received, not what thou hast devised ...짧은 발췌문 보기 - 도서 정보 - 내 서재에 추가하기

Belle Assemblée: Or, Court and Fashionable Magazine; Containing Interesting ...‎ - 229 페이지

1815
However, we think all the trimmings will be superseded by the trimming which is
invented by Mrs. Bell. Pelisses are seldom worn unaccompanied by a shawl or ...전체보기 - 도서 정보 - 내 서재에 추가하기

Greek Literature: Greek literature in the classical period : the poetics of ...‎ - 416 페이지

저자: Gregory Nagy - 2001 - 561 페이지
... 'nol inhabited' (221), a detail which is invented by Sophocles? My second
point will be to underline a remarkable coincidence. ...일부보기 - 도서 정보 - 내 서재에 추가하기

Tiedemann's Record of Infant-life‎ - 25 페이지

저자: Dietrich Tiedemann, Bernard Perez, Frank Louis Soldan - 1890 - 46 페이지
... becomes gradually restricted by the growth of another language, which is
invented by each child and which is capable of endless individual variation. ...짧은 발췌문 보기 - 도서 정보 - 내 서재에 추가하기

History of the Reformation in the sixteenth century‎ - 10 페이지

저자: Jean Henri Merle d'Aubigné, Henry Beveridge, Henry White - 1845
By the religion of the priest, I mean that which is invented by the priest for
the glory of the priest, and is ruled over by a sacerdotal caste. ...전체보기 - 도서 정보 - 내 서재에 추가하기

The Civil engineer and architect's journal‎ - 53 페이지

1859
The new construction of switches described in the following paper, which is
invented by Mr. Edwin Thompson and Mr. William Nicholson, of York, ...전체보기 - 도서 정보 - 내 서재에 추가하기
결과 페
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1-- Speaking of the general process of invention, not any specific one already accomplished.
2-- As #1
3-- A literary device.
4-- As #1
5-- As #1
6-- A usage of the English of 2 centuries ago, 1815
7-- It is an adjective

8-- As #1
9-- As #1-- actually, it is a duplicate hit on #1
10-- A usage of one and a half centuries ago (1859)

Now please consider this topic closed.
Thank you very much. For all intended purposes, the topic is closed. I just want to mention that what I listed as what I came up (with) when I did a Google Book Search was just one screen-ful of entries (sentences?) and there were many more. Thank you for your help.
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Good, thank you. Like Alice's Restaurant, you can get almost anything you want at Ms Google's. By the way, the phrases is 'to/for all intents and purposes'.
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